A heterogeneous solid stress model based on the energy minimization multiscale (EMMS) model is developed. The EMMS model is used in the multiscale decomposition of a heterogeneous gas-solid system, and the local flow field inside a computational cell can thus be divided into a series of dense phases and a dilute phase with uniform solid distributions. With the solid stress model for each phase, a heterogeneous, EMMS-based solid stress can be determined by accounting for subgrid structure information. Furthermore, this heterogeneous solid stress model is integrated into the multiphase particle-in-cell (MP-PIC) method and implemented with in-house MP-PIC codes. MP-PIC simulations for a circulating fluidized bed (CFB) riser and a bubbling fluidized bed (BFB) show that combining the heterogeneous solid stress model and drag model gives results that best agree with experimental data, even with coarser meshes and larger coarse-grain parameters, benefiting industrial-scale computational fluid dynamics simulation. (C) 2019 Elsevier B.V. All rights reserved.