Based on the calculation of the survival probability, equations describing the kinetics of phase transformation with nucleation and growth mechanism are derived for general cases by including the temporal and spatial dependence both for the nucleation rate and for the growth rate. Particularly in this study, the crystallographic relationship in the growth is taken care of. For the simple case, in which the growth rate in the crystallographically identical directions are the same and the shape of grains remains congruent during the crystal growth, the influence of the shape factor on the kinetics can be determined for grains of different contours. The application to epitaxial growth yields the coverage quotient of a certain plane in the deposited crystals as a function of the reaction time and the position. Also the thickness distribution during the deposition can be determined. The exploration of the relationships between the growth kinetics and the crystallography is helpful to obtain reliable information about the mechanisms of nucleation and growth from the evaluation of the measurements. ©1997 American Institute of Physics.