The article presents results of the numerical analyses of the fragmentation warhead, which is one of the key elements of the missile used to combat anti-tank missiles. The fragmentation warhead is composed of such elements as outer casing, inner casing, explosive material and fragmentation liner. The fragmentation liner is built from steel spheres or cylinders embedded in epoxy resin. As a result of the explosive material detonation the pressure wave is generated, which affects the liner, causes its fragmentation, and drives each splinter. In order to perform numerical analyses the model of the cylindrical fragmentation warhead with a diameter of 80 millimetres and a length of 100 mm was prepared. The fragmentation liner consists of steel spheres with a diameter of 5 mm. It was assumed in simulation that the detonating material is the plastic explosive C4. The influence of the position of the explosive charge detonation initiation point of the fragmentation warhead on its effectiveness was studied. Effectiveness was evaluated by measuring the maximum speed obtained by the fragments and their spatial distribution. A three-dimensional model of the studied system has been prepared using the MSC Patran software and the numerical analyses were performed using the finite element method with explicit scheme of the time integration implemented in the LS-Dyna solver. To model gas domain Arbitrary Lagrangian-Eulerian (ALE) method was used and interaction between gas and solid body was modelled with FSI coupling.