A theoretical expression for the total cross section of pion induced reactions of the form ( π, π n) and ( π, πp) has been deduced on the basis of the impulse approximation and one-step knock-out mechanism. In the derivation, both the elastic and inelastic interactions have been taken into account. The expression has been applied to the reactions 12 C(π −, π − n) 11 C, 12 C(π +, π + n) 11 C, 19 F(π −, π − n) 18 F, 40 Ar(π −, π − 39 Cl, 65 Cu(π −, π − n) 64Cu and 181 Ta(π −, π − n) 180 Ta for energies 0.08 – 2.0 GeV. The agreement of the calculated values with the experimental data is found to be good. The first resonance peak in all the cases appears to be shifted towards the lower energy side of the free particle pion-nucleon resonance peak.