An investigation into the relative stabilities and equations of state of stoichiometric FeS was conducted using first-principles pseudopotential calculations. These calculations were based on density functional theory and performed using ultrasoft Vanderbilt pseudopotentials within the generalized gradient approximation. We have identified four stable polymorphs of FeS along the 0 K isotherm as a function of pressure: troilite, an orthorhombic MnP-type structure, a monoclinic structure, and a CsCl-type structure. The calculated internal energy as a function of volume for each polymorph was fitted to 4th order logarithmic and 3rd order Birch-Murnaghan equations of state, yielding values for the bulk modulus, K, and its first and second derivatives with respect to pressure, K′ and K′′. These equations of state may be used to characterize models of planetary cores.