An analytical model is developed for the startup transient of asymmetrical flat-plate and disk-shaped heat pipes. The model solves the proper transient heat conduction equations for the heat pipe wall and liquid-wick regions. A quasi-steady state, pseudo three-dimensional approximation is used for the vapor transient behavior. The heat transfer within the wall and liquid-wick regions is coupled with the vapor phase at the liquid-vapor interfaces. Analytical solutions of temperature, vapor velocity, and vapor pressure distributions are obtained based on an in-depth integral method. Results covering the entire startup transient are presented for disk-shaped and flat-plate heat pipes.