Heat Pipe is a thermodynamic device which transports heat from one location to another with a very small temperature drop. Entropy generation can be considered as a significant parameter on heat pipe performance. Major reasons for entropy generation in a heat pipe system are temperature difference between cold and hot reservoirs, frictional losses in the working fluid flows and vapor temperature/pressure drop along heat pipe. The objective of the present work is to estimate the entropy generation in a flat heat pipe. A computational model is developed for the analysis of the transient operation of a flat heat pipe. The analysis involves the solution of two dimensional continuity, momentum and energy equations in the vapor core with the transport equations for a porous medium in the wick. The entropy generation depends on both temperature and velocity variations of vapor and liquid. Alternating Direction Implicit (ADI) scheme is used to convert the partial differential equations into finite difference equations. A code is developed in C language to solve the system of linear and non linear equations. Variation in temperature, pressure and velocity fields are obtained as a function of time by solving the system of equations using the developed code. The temperature and velocity distributions in the heat pipe are employed for estimating the entropy generation rate in the system.