Summary: We obtain a generalized Neumann solution for the two-phase fractional Lamé-Clapeyron-Stefan problem for a semi-infinite material with constant boundary and initial conditions. In this problem, the two governing equations and a governing condition for the free boundary include a fractional time derivative in the Caputo sense of order \(0<\alpha\leq 1\). When \(\alpha \nearrow 1\) we recover the classical Neumann solution for the two-phase Lamé-Clapeyron-Stefan problem given through the error function.