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This paper presents a formulation of the multicontingency transient stability constrained optimal power flow (MC-TSCOPF) problem and proposes a method to solve it. In the MC-TSCOPF formulation, this paper introduces a modified formulation for integrating transient stability model into conventional OPF, which reduces the calculation load considerably. In our MC-TSCOPF solution, the primal-dual Newton interior point method (IPM) for nonlinear programming (NLP) is adopted. Computation results on the IEEJ WEST10 model system demonstrate the effectiveness of the presented MC-TSCOPF formulation and the efficiency of the proposed solution approach. Moreover, based on quite convincing simulation results, some phenomena occurred when considering multicontingency are elaborated.