The behaviour of the critical current density, J c, of PbMo 6S 8 and SnMo 6S 8 monofilamentary wires with external transverse compressive stress, σ t, and axial tensile stress, σ a, was investigated. Varying the reinforcing steel content in the wire matrix, different axial prestress states, e.g. the compressive, tensile and unstressed state were realized. The observed variation of J c, versus σ a was significantly smaller compared with that of Nb 3Sn wires, which is explained by the higher upper critical magnetic field, B c2, of the Chevrel phase. The elastic strain range of 0.6–0.8% (with 0.2% compressive prestrain of the filament) fulfils the requirements for future technical applications of this type of wire material. The effect of transverse applied compressive stress, σ t, on I c and B c2 ∗ of the Chevrel phase wires was investigated in magnetic fields up to B = 22 T and T = 4.2 K. Analogous to Nb 3Sn wires, a strong degradation of the critical current density with σ t was observed. As for the axial tensile stress, the influence of σ t on J c is found to increase with the applied magnetic field. At 20 T the transverse compressive stress effects reduce J c about twice as much as the axial tensile stress. At present externally steel reinforced PbMo 6S 8 wires can be compared with Nb 3Sn wires, the effect of transverse stress appears to be considerably smaller in the Chevrel phase wire, possibly as a consequence of the higher upper critical field with respect to Nb 3Sn.