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In this paper, the problem of identification of critical k‐line contingencies that fail one after another in quick succession that render large load shed in the power system is addressed. The problem is formulated as a mixed‐integer non‐linear programming problem (MINLP) that determines total demand that cannot be satisfied under various k‐line removal scenarios. Due to the large search space of the problem, the solution through enumeration is intractable. Two algorithms are proposed using a proposed power flow sensitivity and a topological metric to identify a reduced number of k‐line contingencies that initiate cascading overload failure and islanding of power system respectively, that are used to solve the MINLP iteratively for identification of critical k‐line contingencies. The algorithms identify a reduced number of k‐line contingencies in linear time as compared to the exponential time complexity of brute‐force search for solutions of the MINLP. Case studies show that the proposed algorithms significantly reduce the search space and the computation time of the MINLP problem to find the most critical k‐line contingency in the IEEE 30 and 118 bus systems at 2≤k≤4$2 \le k \le 4$ that are also obtained in the list of k‐line contingencies identified using the proposed algorithms.