Boiling up of metastable liquid on the surface of a cylindrical heater is studied at high superheating, when the evaporation front is formed. Boiling up begins with formation of a spherical bubble on the heater wall. Evaporation fronts propagating along the heater with the constant velocity are formed due to development of interfacial instability. The mathematical model describing the growth of a spherical bubble and vapor cavity behind the evaporation front is developed. Results of numerical simulation agree with available experimental data.