We present two different theoretical models for the formation of three-dimensional (3D) quantum dot like islands in Stranski-Krastanov mode. Both models treat the effect of strain in a similar manner. The first model is a kinetic Monte Carlo simulation which is based on randomly selected surface hops of single adatoms. A crystal lattice of fee-type is considered and the consequences for the simulation algorithm are discussed. We find that simulated 3D islands are shaped as truncated pyramids. The: second model is based on coupled mean-field rate equations describing the island density and the evolution of island volume. Several growth regimes can be distinguished in the calculation results. In a 2D growth regime at low coverages, the island size distribution is broad, the average island size increases with deposition time, and islands are approximately one monolayer high. The situation changes at higher coverages. Here, the island size distribution becomes small, the lateral island size is constant, the island height increases with time, and, finally, 3D islands are formed.