This work uses the inverse matrix modification lemma to perform contingency analysis of transmission lines and power transformers of an electric power system. This analysis may be used for planning and operation studies of an electrical energy system. The inverse matrix modification lemma provides directly the inverse matrix for each contingency known the base case inverse matrix. This fact represents a reduction of computational efforts in contingency studies. A Matlab program was developed to contingency analysis using the linear active power flow method and the inverse matrix modification lemma. Results were compared with those ones obtained with the inversion of for each contingency, and with those of Anarede program.