In order to provide new experimental facts required for constructing a nonlinear constitutive equation for solid polymers, some tests were conducted on amorphous polymers of polycarbonate and poly(methyl methacrylate) and for a crystalline polymer of polyoxymethylene under various strain paths such as compression, torsion and combined tension-torsion. It is shown that 1) the stress-strain behavior for the strain paths without strain reversal is described well not only for amorphous polymers, but also for crystalline polymers by an overstress theory proposed by Krempl, and 2) at the strain paths with strain reversal, the stress responses are considerably different from what is expected for the stress responses of metals and their alloys.