Abstract: A new smoothed elastic bimodular constitutive relationship is presented, thus the sensitivity of stiffness matrix with respect to displacement can be obtained conveniently. A FEM and sensitivity analysis based numerical model is developed to solve direct problems of truss structures with dual extensional/compressive modulus, and Newton-Raphson algorithm is employed in the solution process. By utilizing the solutions of direct problems, the identification of bimodulus is realized via an ant colony algorithm. Numerical verification with noisy data is provided with satisfactory results.