The Vicsek model [1] is a very popular minimalist model to study active matter with a number of applications to biological systems at different length scales. With its off-lattice implementation and the periodic boundary conditions, it aims at the analysis of bulk behaviour of a limited number of particles. To expand the applicability of the model to further biological systems, we introduce an on-lattice implementation of the model and analyse its behaviour for three different geometries with reflective boundary conditions. For sufficiently fine lattices, the model behaviour does not differ between off-lattice and on-lattice implementation. The reflective boundary conditions introduce an alignment of the particles with the boundary for low levels of noise. In a pipe geometry, this causes swarms to move along the pipe. In a squared box, we discovered that the edges act as swarm traps.The trapping shows a discontinuous noise dependence. Below a critical noise value, all particles are trapped and above the critical value, no trapping occurs. In a disk geometry, the boundary alignment creates an ordered rotational state. We show that this state is well described by a novel order parameter. Our results present a detailed characterisation of the behaviour of the Viscek model in confined environments with reflective boundary conditions. This provides the basis for an application of the Vicsek model to biological questions that cannot be addressed with the current version of the model.