Vertical cavity surface-emitting (VCSEL) arrays offer an attractive platform to develop a photonic Ising computer due to their scalability and compact physical size. Ising interactions can be encoded between VCSELs through mutual optical injection locking, with the polarity of the interaction determined by the presence or absence of a half-wave plate in the optical path, and the bit itself represented by polarization state. The performance of this approach is investigated computationally by extending the spin-flip model to describe a system of mutually injection locked VCSELs for 2-, 3-, and 4-bit Ising problems. Numerical simulations demonstrate that the modeled system solves the given Ising problems significantly better than chance, with critical parameters in the model identified as crucial for achieving an unbiased Ising solver. The quantum well gain anisotropy parameter as well as the ratio of phase anisotropy to decay rate of the local carrier number causes the system to favor particular Ising configurations over others, but this may not prohibit the system from reaching the ground state.