Elastic properties of Fe-P ordered system (the bulk modulus and the theoretical strength under isotropic tension) are computed by means of ab initio computational program code VASP. Different configurations and relative amounts of constituent atoms are considered in the crystal cells of known stable phases as well as of some hypothetical structures. The influence of a relative content of P in the alloy on computed properties is studied. Magnetic ordering is taken into account by means of collinear spin-polarization. The results of calculations reveal that, somewhat surprisingly, no dramatic changes of elastic moduli are to be expected up to the 67% atomic concentration of P.