Based on a suggested computer model, the loss of morphological stability and dendritic growth in systems with isotropic surface kinetics and the linear dependence of the growth rate on the supersaturation have been studied. It is shown that, in such a formulation of the problem, the changes in the main morphological types are associated with the variation of the kinetic crystallization coefficient. The growth rate and fractal dimension of crystals are studied as functions of the kinetic crystallization coefficient, and the growth rate and mass of crystals are studied as functions of supersaturation. The problems associated with the variation of distances between the secondary dendrite branches are considered. The results obtained within the model are applied to systems with anisotropic surface kinetics.