Abstract: Based on the generalized ubiquitiformal Cantor set,a ubiquitiformal constitutive model for a bi-material rod was proposed. Effect of both aggregate volume ratio and aggregate gradation can be taken into account, and then the explicit analytical expressions for calculating effective elastic modulus was obtained. The numerical results for concrete were found to be in good agreement with previous experimental data.Moreover, in the ubiquitiformal model, the interfacial displacements between the two materials are continuous, which avoids the difficulty of the discontinuous interfacial displacements in previous fractal models.