In this master thesis we study diffusion of particles in a membrane by means of numerical simulations and theoretical analysis. The particles are randomly distributed in two membranes set parallel to each other and are able to diffuse within membrane as well as make bridging complexes spanning the two membranes which make the particles in a complex immobile. We proposed expressions for the density of bridging complexes and for the effective diffusion coefficient of the particles. Using Monte Carlo simulations we investigated the dependence of the aforementioned physical quantities on the physical parameters of the system. These are intrinsic mobility of particles on both membranes, binding energy of the formation of the bridging complex and the concentration of particles on both membranes. As a notable result we report the increase in effective diffusion coefficient with the increase of the concentration of diffusing particles on the same membrane. A similar phenomenon has already been detected in simulations and studied analytically in an analogous system with imobilized particles on one of the membranes [1]. The analytical expressions for the diffusion coefficient we proposed here are in agreement with simulation data for low particle concentrations. Disagreement of the simulation data and analytical models at high particle concentrations hints on possible future approaches to modelling membrane diffusion in biological systems.