A necessary prerequisite for a successful theory-guided up-scale design of materials with application-driven elastic properties is the availability of reliable homogenization techniques. We report on a new software tool that enables us to probe and analyze scale-bridging structure-property relations in the elasticity of materials. The newly developed application, referred to as SC-EMA (Self-consistent Calculations of Elasticity of Multi-phase Aggregates) computes integral elastic response of randomly textured polycrystals. The application employs a Python modular library that uses single-crystalline elastic constants C
ij as input parameters and calculates macroscopic elastic moduli (bulk, shear, and Young's) and Poisson ratio of both single-phase and multi-phase aggregates. Crystallites forming the aggregate can be of cubic, tetragonal, hexagonal, orthorhombic, or trigonal symmetry. For cubic polycrystals the method matches the Hershey homogenization scheme. In case of multi-phase polycrystalline composites, the shear moduli are computed as a function of volumetric fractions of phases present in aggregates. Elastic moduli calculated using the analytical self-consistent method are computed together with their bounds as determined by Reuss, Voigt and Hashin-Shtrikman homogenization schemes. The library can be used as (i) a toolkit for a forward prediction of macroscopic elastic properties based on known single-crystalline elastic characteristics, (ii) a sensitivity analysis of macro-scale output parameters as function of input parameters, and, in principle, also for (iii) an inverse materials-design search for unknown phases and/or their volumetric ratios.