The critical current (Ic) of six different Nb3Sn multifilamentary wires is investigated as a function of temperature, magnetic field, and strain. A relation for a critical temperature (Tc) that depends on the deviatoric strain is proposed and applied to interpret the results. First, a short review is given on the flux-pinning relations that are used to introduce a strain dependent Tc in a relation for the Ic as a function of field and temperature. The conductor samples are investigated in two different deformation states, namely, in a spiraled shape on a Ti sample holder and a straight section soldered onto a brass substrate. The brass substrate is used to apply a compressive or tensile axial strain to the conductor. The Ic in the different samples prepared from a single conductor type can be described very well with a single set of critical properties and strain parameters. In particular, in the strain regime where the matrix deformation is limited and the superconductor is axially compressed, the proposed strain relation is very accurate. The small variation in the strain parameter between the six conductors investigated suggests that this strain parameter is an intrinsic property of Nb3Sn.