Systematic studies of the so-called positron accumulation effect for samples with particles embedded in a matrix are reported. This effect is related to energetic positrons which penetrate inhomogeneous medium. Due to differences in the linear absorption coefficient, different amounts of positrons are accumulated and annihilate in the identical volume of both materials. Positron lifetime spectroscopy and Doppler broadening of the annihilation line using Na-22 positrons were applied to the studies of the epoxy resin samples with embedded micro-sized particles of transition metals, i.e., Ni, Sn, Mo, W, and nonmetal particles, i.e., Si and NaF. The significant difference between the determined fraction of positrons annihilating in the particles and the particle volume fraction indicates the positron accumulation effect. The simple phenomenological model and Monte Carlo simulations are able to describe the main features of the obtained dependencies. The aluminum alloy with embedded Sn nanoparticles is also considered for demonstration differences between the accumulation and another related effect, i.e., the positron affinity.