Continuum and rarefied vapor flows co-exist along the heat pipe length for most of the startup period. A two-region model is proposed in which the vapor flow in the continuum region is modeled by the compressible Navier-Stokes equations, and the vapor flow in the rarefied region is simulated by a self-diffusion model. The two vapor regions are linked with appropriate boundary conditions, and the heat pipe wall, wick and vapor flow are solved as a conjugate problem. The numerical solutions for the entire heat pipe startup process from the frozen state are compared with the corresponding experimental data with good agreement.