The Bible contains no specific direction on the practice of cremation. There is no Bible command regarding either burial or cremation of the dead. Generally, there are no explicit verses in the bible that promote or denounce the act of cremation. However, some believe keeping ashes in ones’ home makes them unclean. Probably, the views come from Numbers 19, Numbers 5, and Leviticus 5.
Here's a review of some of those passages.
Numbers 19:9-11 – "A man who is clean shall gather up the ashes of the heifer and put them in a ceremonially clean place outside the camp. They are to be kept by the Israelite community for use in the water of cleansing; it is for purification from sin. The man who gathers up the ashes of the heifer must also wash his clothes, and he too will be unclean till evening. This will be a lasting ordinance both for the Israelites and for the foreigners residing among them. Whoever touches a human corpse will be unclean for seven days . . . If they fail to purify themselves after touching a human corpse, they defile the Lord's tabernacle. They must be cut off from Israel."
Numbers 5:1 - 4 – The Lord said to Moses, "Command the Israelites to send away from the camp anyone who has a defiling skin disease or a discharge of any kind, or who is ceremonially unclean because of a dead body. Send away male and female alike; send them outside the camp so they will not defile their camp, where I dwell among them." The Israelites did so; they sent them outside the camp. They did just as the Lord had instructed Moses.
Leviticus 5:2-6 "'If anyone becomes aware that they are guilty—if they unwittingly touch anything ceremonially unclean (whether the carcass of an unclean animal, wild or domestic, or of any unclean creature that moves along the ground) and they are unaware that they have become unclean, but then they come to realize their guilt; or if they touch human uncleanness (anything that would make them unclean) even though they are unaware of it, but then they learn of it and realize their guilt; or if anyone thoughtlessly takes an oath to do anything, whether good or evil (in any matter one might carelessly swear about) even though they are unaware of it, but then they learn of it and realize their guilt—when anyone becomes aware that they are guilty in any of these matters, they must confess in what way they have sinned. As a penalty for the sin they have committed, they must bring to the Lord a female lamb or goat from the flock as a sin offering[a]; and the priest shall make atonement for them for their sin.'"
The Bible does report instances of the faithful burying their dead. Abraham went to great lengths to secure a burial place for his wife, Sarah. (Genesis 23: 2- 20; 49:29- 32). The Bible also mentions faithful individuals burning the remains of the dead. When King Saul of Israel and three of his sons were killed in battle, their corpses initially remained in enemy territory and were treated dishonorably. Hearing of the situation, faithful Israelite warriors retrieved the bodies of Saul and his sons, burned them, and buried the remains. (1 Samuel 31: 8- 13) The Bible indicates that this was an acceptable way to treat the remains of those men. —2 Samuel 2: 4-6.
Common Misconception: Cremation dishonors the body.
Truth: The Bible says that those who die return to the dust, which is what naturally happens to a corpse when it decomposes. (Genesis 3: 19) Cremation speeds up the process by reducing the body to ashes, or dust.
Common Misconception: In Biblical times, only people in God’s disfavor were burned after death.
Truth: The dead bodies of some unfaithful people, such as Achan and his family, were burned. (Joshua 7: 25) This was an exception rather than the rule. (Deuteronomy 21:22, 23) As noted earlier, the bodies of even some faithful people, such as King Saul’s son Jonathan, were burned after death.
Common Misconception: Cremation prevents God from resurrecting a person.
Truth: Regarding resurrection of the dead, it does not matter to God whether a person’s body was buried, cremated, lost at sea, or eaten by wild animals. (Revelation 20:13) The Almighty can easily re-create a new body for the person. —1 Corinthians 15:35, 38.
A big concern in the Bible is for cleanliness. However, scripture calls us to be in relationship with all people, and to not think so highly of ourselves that we can not associate with people of lower standing. Often those people of lower standing are in messy situations, or unclean situations, and could well be in a place of suffering that we are called to enter into. What is in the heart maters most.
The Bible isn't explicit on the matter of ashes and cremation. Hence, the growing desire for many to be cremated and the churches' willingness to allow it.