The prediction of ply delamination in laminated composites is modeled by using interface elements. The numerical approach is based on the cohesive zone model, which is shown to provide an efficient description of the delamination growth. The theoretical study is performed in quasi-static regime and an implicit finite element scheme is used. A comprehensive 1D example shows that cohesive elements may induce numerical instability and that the use of a viscous regularization is relevant to suppress the instability and to obtain a reasonable numerical convergence. This paper describes a technique that can be used to introduce damping into cohesive zone finite element simulations of crack nucleation and growth, with a view to avoiding convergence difficulties in quasi-static finite element simulations. A new kind of viscous regularization is proposed, which applies to the bilinear debonding model and has a limited rate dependency. An experimental study is performed by using DCB (double cantilever beam) samples for the mode I interlaminar fracture toughness test; a good agreement between numerical predictions and experimental results is obtained.