Advances in multi-material additive manufacturing have opened unprecedented new opportunities for the design and manufacture of lightweight multifunctional structures. The ability to create complex topologies, at a relatively fine resolution, in addition to controlling the material composition on a voxel basis have significantly expanded the design space. To explore this large design space efficiently, accurate and cost-effective modeling tools are essential. In this paper, mechanics-based models for predicting the elastic properties of multi-material 2D and 3D lattice structures are developed or extended. The outcomes are compared with the predictions obtained from finite element models and experimental data. The results reveal that the adapted analytical models demonstrate good accuracy in predicting the elastic modulus of multi-material lattices for relative densities up to approximately 25% while have considerably less computational cost compared to finite element using solid elements (providing the most accurate results in comparison with experiment). Careful consideration of the accuracy of the predictions is necessary for the use of these models for lattices with high relative density values. Besides, several homogenization-based models were studied to investigate their applicability to multi-material lattice structures when the assumption of scale-separation is considered valid. The capability of these models in predicting the whole elasticity tensor and the potential of multi-material lattices in manipulating the anisotropy are demonstrated. Finally, the introduced prediction frameworks are compared in order to provide an overview of their respective advantages and disadvantages in the case of multi-material lattice structures.