The paper presents new failure criteria which can be applied to brittle polymer composites. The criteria can be applied to specimens regardless of whether they have cracks, cutout, or none of them. The new criteria consist of two failure conditions, both of which must be satisfied if failure occurs at any critical location. The first condition is the stress-based failure criterion. This condition of failure determines potential failure locations. For failure to occur, not only a location but also its neighbor should possess criteria favorable to failure. The second condition is related to the neighbor condition, and it is the stress gradient-based failure criterion. This condition states that failure may occur when the cubic power of the effective stress divided by its stress gradient is equal to or greater than the critical failure value of the selected material. The second condition determines the failure path from the failure location. Laminated fibrous composites have different stiffnesses and strengths depending on the orientation of the layers. This paper proposes a way to predict failure strengths of laminates with different layer orientations containing holes if the failure strength is known for a laminate.