In this paper we identify conditions under which the cohomology H*(ΩMξ;k) for the loop space ΩMξ of the Thom space Mξ of a spherical fibration ξ\downarrow B can be a polynomial ring. We use the Eilenberg-Moore spectral sequence which has a particularly simple form when the Euler class e(ξ)∈ Hⁿ(B;k) vanishes, or equivalently when an orientation class for the Thom space has trivial square. As a consequence of our homological calculations we are able to show that the suspension spectrum Σ^∞ΩMξ has a local splitting replacing the James splitting of ΣΩMξ when Mξ is a suspension.