We investigate the thermal evolution of non-spherical primordial gas clouds of mass M=10(6)M.. We study two cases: I) prolate and oblate clouds without angular momentum, 2) initially spherical, oblate and prolate clouds with angular momentum. In the spherical case, the magnitude of the angular momentum is the key quantity which determines the fragment mass. The fragment mass is found to be M greater than or similar to 90M. for 10(-2)less than or similar to lambda less than or similar to 1, where lambda is the cosmological spin parameter. For an oblate shape of initial gas clouds, the angular momentum is almost never important. In the case of prolate clouds with some angular momentum, collapse proceeds in the same way as in the spherical case, and a bounce occurs to form a disk due to the angular momentum. In any case, the estimated ''fragment mass'' must be almost above 90M. for primordial gas clouds with typical angular momentum and typical oblateness or prolateness.
