The well-known Timoshenko beam equations (which include transverse shear deformation and rotary inertia effects) are extended for a wide-flanged structure to include the additional shear lag deformation of the flanges; thus, cross-sections of the beam are allowed to distort instead of remaining plane sections. The effect of relative flange bending (bending of the flanges relative to the web) is also included and the integro-differential equations appropriate to the problem are derived. The frequency equation is given in closed form (neglecting the relative flange bending) and solutions for various values of the nondimensional parameters are given. A reduction of the elementary frequency by as much as 40 percent in the first mode is shown. / Master of Science