Your question involves two issues, burial and cremation. First I'll discuss burial, then I'll discuss cremation.
The requirement to bury the dead is from the verse, “If a man committed a sin worthy of death...you shall surely bury him that day” (Deut. 21:23). The verse, “for you are dust and to dust you shall return” (Gen. 3:19), teaches that ideally a buried body should be in contact with the ground. Upon death, the soul cannot fully depart until the body has completely disintegrated. On the other hand, an abrupt departure would cause the soul great agony. Burial ensures the gradual but eventual decay of the body needed to benefit the soul. Our Sages thus remarked, “Burial is not for the sake of the living, but rather for the dead”.
Burial actually preceded the giving of the Torah. The Midrash relates that God brought before Cain a bird burying another in order to teach him to bury Hevel. Similarly, all of the patriarchs and matriarchs were buried: “and his sons buried [Abraham] (Gen. 25:9-10); “and [Isaac's] sons buried him” (Gen. 35:29); “for his sons...buried [Jacob] (50:13); “Abraham buried Sarah” (Gen. 23:19); “there they buried...Rebecca and...Leah (Gen. 49:31); “and [Jacob] buried [Rachel] in...Beit Lechem (Gen. 48:7).
Even Joseph who died in Egypt “took an oath of the children of Israel saying, God will surely visit you, and you shall carry up my bones from here” (Gen. 50:25). Moses fulfilled the oath (Ex. 13:19) and eventually “the bones of Joseph...they buried in Shechem” (Joshua 24:32). Further, the Talmud teaches that one of the ways a Jew imitates God in performing acts of righteousness is by burying the dead, as God did for Moses, “And He buried him in the valley in the land of Moav” (Deut. 34:6).
After the giving of the Torah, burial became obligatory. Counted as one of the 613 commandments of the Torah, anyone who prevents himself or others from being buried uproots a positive Torah requirement to bury, and also transgresses a negative Torah prohibition of leaving a body unburied. In fact, the Talmud states that anyone who orders before his death that his body should not be buried, his order must be disregarded, and this is the halacha.
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In Judaism, burning of the human body is considered a disgrace. Regarding the execution of the wicked Achan and his sons and daughters the verse states: "And all Israel stoned him with stones, and burned them in the fire....So God rescinded His anger" (Joshua 7:25). Similarly, the righteous King Yoshiyahu “executed the priests of idol worship upon their altars and burned their bones upon them” (2 Kings 23:20). The Talmud relates how after evil Yehoyakim suffered a “donkey's burial”, his skull was eventually found and degradingly burnt. Burning the human body is so disgraceful that God declared, “I will not turn away [Moav's] punishment, because he burned the bones of the King of Edom into lime” (Amos 2:1).
Not only is burning the
