We present a grid of evolutionary computations covering the major phases of H and He burning for stars having masses between 3 and 9 M⊙. The computations have been performed for two different assumptions on the amount of original helium (Y = 0.23 and 0.27) and for the three values of the metallicity Z = 0.02, 0.006, and 0.002. All the evolutionary tracks have been computed from the main-sequence phase up to the carbon ignition or to the reignition of the H shell which marks the start of the thermally pulsating phase. Comparison is made with the results of previous investigations, discussing the origin of some relevant variations. Extensive tabulations of the evolutionary results are reported and shortly discussed. The starting luminosity of thermal pulses has been identified for 23 models which do not ignite carbon, supporting previous evaluations of this parameter given in the literature. However, we suggest that the second dredge-up could be more efficient than usually assumed, with sizable consequences on the limiting magnitude for thermal pulsating structures. Theoretical values for the limiting mass for carbon ignition are finally shortly discussed.