This thesis presents the results of an experimental investigation into the strength of brickwork under biaxial tension-compression. Since there is insufficient experimental evidence available on the strength of brickwork under biaxial stress to explain the behaviour of brick masonry walls under in-plane loads, experiments were carried out on one-sixth scale model brickwork panels under uniform stress conditions. An idealized failure surface is suggested based on experimental results, and the effect of shear bond strength and tensile bond strength on the results is discussed. An iterative plane stress finite element computer programme incorporating the above information is used to simulate the in-plane behaviour of brickwork. Brickwork is treated as an elastic, isotropic material with limited capacity when stressed in a state of biaxial tension-compression. The model reproduces the non-linear behaviour of masonry produced by progressive cracking. Shear wall tests have been used to test the validity of the analytical model. Sensitivity analysis of the elastic constants used in the model are performed to illustrate their influence on the calculated stresses. The influence of the stress distribution on shear wall behaviour, and the derivation of a failure criterion for local failure in masonry shear walls, are described. This criterion, in terms of the vertical stress and shear stress at a point, has been derived for particular values of horizontal stress from the three dimensional surface mentioned above. The effect of the shape of the specimen, testing technique, and boundary conditions on the shear strength of masonry panels is discussed.