In this paper, an analytical solution of a tapered bimodular beam has been developed. An Euler-Bernoulli beam theory with shear deformations has been utilized to obtain the solution. The bimodular beams are different from those unimodular beams in having two different moduli of elasticity one in compression and another in tension. A verification for the solution has been performed using FEM analysis with ANSYS. The results of the program were very close the results of the analytical solution presented in this paper.