This paper deals with numerical and analytical modelling of a diamond or silicon particle embedded in a metallic matrix. The numerical model of an elastic particle in a metallic matrix was created using the Abaqus software. Truncated octahedron-shaped and spherical-shaped diamond particles were considered. The numerical analysis involved determining the effect of temperature on the elastic and plastic parameters of the matrix material. The analytical model was developed for a spherical particle in a metallic matrix. The comparison of the numerical results with the analytical data indicates that the mechanical parameters responsible for the retention of diamond particles in a metal matrix are: the elastic energy of the particle, the elastic energy of the matrix and the radius of the plastic zone around the particle. An Al-based alloy containing 5% of Si and 2% of Cu was selected to study the mechanical behaviour of silicon precipitates embedded in the aluminium matrix. The model proposed to describe an elastic particle in a metallic matrix can be used to analyze other materials with inclusions or precipitates.