The paper is focused on a detailed numerical analysis of the stress field in specimens used for the wedge splitting test (WST) which is an alternative to the classical fracture tests (bending, tensile) within the fracture mechanics of quasi-brittle building materials, particularly cementitious composites. The near-crack-tip stress field in the WST specimen is described by means of constraint-based two-parameter fracture mechanics in the paper. Different levels of constraint in the vicinity of the crack tip during fracture process through the specimen ligament are characterized by means of the T-stress. Two basic shapes of WST specimen – the cube-shaped and the cylinder-shaped one – are investigated and the determined near-crack-tip stress field parameters are compared to those of compact tension (CT) specimens according to the ASTM standard for classical and round geometry. Particular attention is paid to the effect of the compressive component of the loading force (complementing the splitting force) acting on the loaded side of the specimen and its reaction from the opposite part of the specimen on the stress field in the cracked body. Several variants of boundary conditions on the bottom side of the specimen used for this kind of testing procedure are also considered. The problem is solved numerically by means of the finite element method and results are compared with data taken from the literature.