We revisit the problem of translation-invariant pressurized membranes that are squeezed without friction between several planes, all parallel to the axis of translation-invariance (such problem involves material and geometric nonlinearities, including contact). Quite remarkably, it was shown by De Simone and Luongo (2013) that such problems simplify considerably under the plane strain assumption. Indeed, the complex initial boundary-value problem reduces to a simple set of non-linear, algebraic equations. We argue that in many practical cases, the plane strain assumption does not hold. Instead, we introduce the generalized plane strain assumption, that is necessary to account for the longitudinal equilibrium of the membrane. We show how the equations of De Simone and Luongo (2013) are modified, while remaining extremely simple. We thus define an extended class of problems that become (nearly) tractable analytically.