A stochastic model is proposed and kinetic equations are derived to describe the boiling process on a solid surface. The model considers bubble growth at discrete nucleation sites and accounts for interactions between adjacent sites. The model is valid for initial stages of nucleate boiling when vigorous surface boiling has not yet commenced. The interactions considered are the seeding with vapor of inactive sites by bubbles at neighboring active sites, and the deactivation of active sites by thermal interference from neighboring sites. The stochastic model is applied in Monte Carlo simulation, employing parameters obtained from experimental results, to predict bubble emission rates and heat fluxes from the surface. The numerical results predict the presence of many permanently inactive sites, the formation of active-site clusters, and the rise in the density of active sites with increase in overall heat flux. The description of the homogeneous nucleate boiling process in terms of dynamic percolation theory is presented.