An approach to calculating the exitation cross sections and rate coefficients for a wide class of transitions in atoms and ions induced by collisions with heavy charged particles in considered. Calculations were carried out in terms of the Born approximation in the impact parameter representation with the normalization and Coulomb repulsion (in the case of an ionic target). Transitions between levels in He and He-like ions without changes of the principal quantum number are considered for n=2–4. Fitting formulas are suggested for transition rate coefficients. Tables of cross sections and parameters of fitting formulas are given for He and C4+.