Results from numerical simulations of a projectile penetrating a concrete target are discussed in this report. The simulations are performed with the 2D and 3D Autodyn software, and the mechanical properties of the concrete are described with the RHT model. This advanced material model incorporates elastic limit, failure and residual strength of the concrete under pressure. Advantages and disadvantages of the use of Lagrange elements and the SPH meshless method for the targets are discussed, and comparisons between the methods are made. The use of a combination of Lagrange elements and SPH nodes for the targets are also discussed. Advantages with 3D simulations are that penetration models with e.g. oblique impact, varying angle of attack and reinforced concrete targets can be studied. This is not possible with a 2D model. However, 3D simulations require a large number of elements/nodes. Therefore, the use of parallel processor systems are necessary to reduce the time needed for the computations, and a parallel processor system with four processors is tested to reduce the required simulation time for the 3D simulations. The numerical results are, when possible, compared to experimental ballistic tests conducted in 1999. In summary, the use of 3D meshless SPH models combined with the RHT material model for concrete seems promising for future research of concrete penetration, e.g. studies of dual charge warheads and improved protective structures.