This work is a report of study carried out on the rate of evaporation from a liquid surface. In the theoretical approach, the Boltzmann transport equation with the simplified collision terms as modelled in the BGK equation was made use of. This collision term is taken to be the difference between the Maxwellian distribution of molecular velocities under equilibrium condition and the actual distribution function under non-equilibrium condition. The problem was formulated for both single component and two component cases. The resulting Itegro-differential equations were simplified to a set of ordinary differential equations. These were solved numerically with appropriate boundary conditions to obtain the distribution functions and the variation of the different properties like temperature, pressure and number density. The rate of evaporation was also predicted. The evaporation coefficients that occur in the equations has to be determined experimentally. Experiments were conducted with pure water for the single component case. For the case where an inert gas is present nitrogen was used as the inert gas. From the results obtained the evaporation coefficients were calculated.