The finite element method is used to to study progressive failure aspects of laminar composite skewed hypar shells with straight edges employing the eight-node isoparametric element in linear and elastic ranges under uniformly distributed static loading. A stiffness decrease scheme is proposed in which the stiffness properties of the failed element are gradually reduced resulting in redistribution of eveloping stresses on the extent of damage it accumulates. Specific numerical problems of earlier investigators are solved to validate the present approach. Numerical experiments are further carried out for different parametric variations, including some complicated boundary conditions and stacking orders of practical importance to obtain the first ply and progressive failure loads. Well accepted failure criteria are used to evaluate the failure loads and its development. Progressive failure in hypar shells are examined to arrive at some conclusions useful to the practicing engineers regarding tailoring guidelines of laminar composites and planning of nondestructive test programs for their health monitoring.