Due to the differences in Young's moduli under the tensile and compressive loadings for a rock-like and asphalt-mixture materials, the analysis becomes difficult as all coefficients in Hook's law are dependent on the stress state in the field. In this paper, the meshless method is formulated for the first time to evaluate a cracked structure made of bimodular materials. In general, there are four stress zones in the field determined by the principal stresses. It is known that for classical elasticity (single modulus material), the stresses are ...