A basic model is presented for parallel folding of two flexible layers under compression, obliged by the presence of overburden pressure to remain in contact along their length. The nonlinear effect of friction is fully explored via a quasi‐energy formulation and the calculus of variations, leading to representation as an ordinary differential equation. The outcomes of both theoretical and numerical modelling are compared with a simple Galerkin approximation. The significance of friction‐induced jamming is explored. Comparisons between the linearized differential equation under the nonlinear boundary conditions and the full nonlinear formulation indicate that the linearization captures most of the significant behaviour.