This paper presents 4-, 5-, 6- and 7-node isoparametric Timoshenko beam elements for modeling constant and varying cross-section thick and thin beams with various boundary conditions. Numerical integration is employed to determine the mass and stiffness matrices to facilitate modeling of varying cross-section beams. The accuracy of each proposed element is illustrated by determining the natural frequencies of: Thick and thin beams with constant and varying cross-section; linearly tapered cantilever circular tube with small wall thickness; chimney structure; and of a four-bar mechanism. In all examples, the results obtained using the proposed elements are compared, whenever available, with exact solution and with solutions determined when other elements available in the literature are used. The proposed elements did not cause shear locking when tested on thin beams of aspect ratio 500.

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