The contact melting process of solid phase change material (PCM) has essential applications in some energy storage systems, which is related closely to the heat resource’s geometry and thermal boundary conditions. The contact melting of PCM in a horizontal elliptical tube under the second kind of thermal boundary condition, namely the constant surface heat flux, was investigated analytically. The analysis model is proposed based on the contact melting lubrication theory, and the model deduces the basic dimensionless equations. The variation rules of parameters such as contact melting speed, melting completion time, and boundary layer thickness distribution are obtained for the different heat fluxes. The influences of the elliptical heat resource geometry boundary and the compression coefficient on these melting parameters were also analyzed. The results include the contact melting inside a horizontal circular tube. Compared with the contact melting under the first kind of thermal boundary condition, the constant surface temperature, some significant conclusions are drawn.