Main objectives In this study, we design an efficient and fully scalable parallel algorithm to implement the 3D nonperiodic homogenization method for elastic media upscaling, so as to make it easily applicable to seismic full waveform modelling and inversion on large-scale 3D problems. New aspects covered Instead of mathematical proofs and derivations of the homogenization theory, this study is developed from the application point of view. A fully scalable parallel conjugate-gradient iterative scheme is introduced into the 3D non-periodic homogenization process for solving its elastostatic equation systems and applying the low-pass filtering (here we use a cascade of elliptic PDE-defined Bessel filters to approximate the conventional convolution-based Gaussian low-pass filtering without the sacrifice of effectiveness).