This question came during our study on life after death for those who believe in Jesus.

Here’s what I found about the history of cremation:

Scholars today quite generally agree that cremation probably began in any real sense around 3000 B.C. - and most likely in Europe and the Near East. Later cremation began to spread across northern Europe, as evidenced by particularly informative finds of decorative pottery urns in western Russia among the Slavic peoples. From there, the practice spread to the British Isles and into what is now Spain and Portugal. Cemeteries for cremation developed in Hungary and northern Italy, spreading to northern Europe and even Ireland. Around 1000 B.C. - cremation became an integral part of the elaborate Grecian burial customs. In fact, it became the dominant mode of disposition by 800 B.C. and was actually encouraged for reasons of health and expedient burial of slain warriors in this battle-ravaged country. By the time of the Roman Empire - 27 B.C. to 395 A.D. - it was widely practiced, and cremated remains were generally stored in elaborate urns in burial buildings. Even though the practice was common among Romans, cremation was rare with early Christians who considered it pagan and in the Jewish culture where traditional burial was preferred. Thus by 400 A.D., as a result of Emperor Constantine's Christianization of the Roman Empire, earth burial had completely replaced cremation except for rare instances of plague or war, and for the next 1,500 years remained the accepted mode of burial.

And here’s my answer to the "is it ‘ok’" part of the question:

Until recently the it was commonly held that cremation is not the ideal method of interment for the Christian. This feeling is not based on any direct command of Scripture, for there is none, but on the practice established in both the Old and New Testaments in which Christ, His apostles, and the Old Testament patriarchs were all buried in traditional body-preserving fashion. Second, since cremation originated as a practice of the pagans (people who believe in different gods, or people who don’t believe in any god), the church did not want to embrace any practices that would associate Christianity with paganism. Furthermore, as Christians we believe (and look forward to) the resurrection of the body, but some thought that cremation does not visually show or express a belief that the body will one day be resurrected.

Given these reasons for earth-burial, we also need to keep in mind that since God has not set down hard and fast rules for burial, we would be wise not do so either. We need to remember that certainly God, who breathed the world into existence, who parted the seas, who calmed the waters, and who raised His own Son from the dead, can renew cremated remains into glorified beings on resurrection day - just as easily as he can renew naturally decayed remains.

It would be logical to assume that the complete lack of biblical instruction on burial would indicate that burial methods aren’t of great concern to God. A Christian could have very valid reasons for either form of burial. The message of the Bible strongly indicates it is one’s personal belief and commitment to Christ in life and not the manner of burial after death that determines where a person will spend eternity.