This article presents a finite element-based study of geometrically non-linear progressive failure analysis of open-hole composite laminates, subjected to combined in-plane and out-of-plane loading. Different ply- and constituent-based failure criteria and material property degradation schemes have been coded in Patran command language and a progressive failure analysis code is developed. Progressive failure analyses of the sample composite laminate, with an open-hole, subject to different combined loading are performed to study the effect of the geometric non-linearity on the first ply failure and progression of failure. For mode independent failure criteria, a method is proposed for the determination of separate degradation factors for fiber and matrix failures which are assumed to occur simultaneously. The results show that under combined in-plane and out-of-plane loading, depending on the load case linear analysis can significantly underestimate or overestimate the failure progression compared to the geometrically non-linear analysis even at low levels of out-of-plane loading.