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The stress‐strain response of crystalline high density polyethylene and of amorphous polycarbonate has been determined in tension and in compression at superimposed pressures up to 1104 MPa(160 ksi). Strain softening occurred in the polycarbonate at low pressures but was inhibited by pressure. Tensile necking occurred in both materials, but was promoted by pressure in polyethylene and inhibited in polycarbonate. The initial modulus, E, and the flow stress, σ, at a given offset strain varied linearly with the mean pressure, P, with essentially the same pressure coefficient, α. Thus, E = (1+αP)E0 and σ = (1+αP)σ0, where E0 and σ0 are values at zero mean pressure. In polyethylene, the coefficient, σ0, was the same in tension and compression, indicating that the strength differential between tension and compression was a simple manifestation of pressure‐dependent yielding. In polycarbonate the coefficient, σ0, was different in tension and in compression, implying an effect due to the third stress invariant or to anisotropy. The results suggest a constitutive model for polymers in which the flow stress is linearly dependent on mean pressure, but in which inelastic volume change is negligible. The results also suggest that the pressure dependence of flow stress in polymers is the same as that of the initial modulus.