Atomic clusters have been proposed as building blocks for tailor-made materials with specific combinations of properties. Growth of such clusters from vapor must be understood to enable one to prepare such materials. Here the process of the cluster growth in expanding copper vapor is analyzed by solving the balance equations for atoms, diatomic molecules, and clusters of different sizes as functions of temperature of buffer gas atoms and clusters. Dependence of the average cluster size at the end of the process on expansion time and the initial number density of atoms is studied. Numerical calculations are performed to obtain the realistic character of change of vapor parameters in a jet nozzle.