Abstract
In this work two-phase Stefan problem for the cylindrical heat equation is considered. One of the phase turns to zero at initial time. In this case, it is difficult to solve by radial heat polynomials because the equations are singular. The solution is represented in linear combination series of special functions Laguerre polynomial and confluent hyper-geometric function. The free boundary is given and heat flux is found. The numerical and approximate test problem is compared graphically. The undetermined coefficients are founded. The convergence of series proved.