We use massive superconducting absorbers made of molybdenum and vanadium as low temperature calorimetric particle detectors. The high resolution of our thermometry system, consisting of a superconducting phase transition thermometer monitored with a dc-SQUID, enables us to detect alpha and gamma particles with large single crystals. Heat pulses generated by passing current through a metal film on the surface of the crystal are used to study the response of the calorimeters. With a 35 g molybdenum single crystal we obtain an energy resolution of 10% FWHM on 5.8 MeV alpha particles at an operating temperature of 120 mK. The observed temperature rise of 1.2 muK is a factor of 8 less than expected from the calculated heat capacity. Using a 15 g vanadium single crystal, the energy resolution on 5.8 MeV a particles is 1.2% FWHM. In this case, the pulse height of 6.1 muK is a factor of 8 smaller than expected from the calculated heat capacity. A possible reason for the large deviations from the expected heat capacity is the presence of hydrogen dissolved in vanadium. Impurities and defects on the surface of the crystals probably contribute also to the heat capacity. The pulse shapes of all observed events are very similar, whether they are created by absorption of alpha or gamma radiation or by an electrically created heat pulse, and consists of two exponential decaying parts. A comparison of the pulse heights of heater and radiation pulses leads us to the conclusion that all the energy deposited in the absorber crystal is converted into phonons.