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In this paper, a finite element model for cracked plane structures, under bending moment, axial and shear forces, is formulated, by employing Euler-Bernoulli and Timoshenko theories. The vibration characteristics of the structures with a single edge crack is investigated using a modified line-spring model and a cracked finite element. For the two different methods considered, the stiffness matrix for a zero-length cracked element and for a l-length cracked element having two nodes and three degrees of freedom is derived, starting from an integration of stress intensity factors. A parametric study of a transverse open crack is carried out for various crack depths and crack locations using the two different theories.