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We investigated the thermal evolution of non-spherical primordial gas clouds of mass $ M=10^6M_\odot $. We studied two cases: 1) 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 $M \gsim 100 M_\odot$ for $10^{-2} \lsim \lambda \lsim 1$, where $\lambda$ is the cosmological spin parameter. For the oblate shape of initial gas clouds, the angular momentum is almost always not important, In the case of prolate clouds with some angular momentum, collapse proceeds in the same way as spherical case, and the bounce occurs to form a disk due to the angular momentum. In any case, the estimated ``fragment mass'', must be above $100 M_\odot$ for the primordial gas clouds with typical angular momentum and typical oblateness or prolateness.

The Fragment Mass Scale of the Primordial Gas Clouds. I: Non-Spherical Pressure-Free Collapse