Abstract: Concrete is a typical quasi-brittle material, and the nonlinear analysis and crack simulation of concrete during loading are still challenging issues. Classical fracture mechanics and damage mechanics describe crack topology from discrete and continuous perspectives respectively, and became two of the most powerful tools for solid crack simulation and prediction problems. Since the beginning of this century, in the phase field theory and peridynamics significant progress has been made in predicting the crack initiation and propagation and nonlinear analysis. Recently, a new nonlocal macro-meso-scale consistent damage (NMMD) model has been developed based on the basic ideas of phase field theory and peridynamics. In this model, the concepts of material point pair are introduced to characterize the meso-scale damage due to deformation. Then the topologic damage which quantifies the degree of discontinuity in macroscopic solid is defined as the weighted average of meso-scale damage in the influence domain. Through the physically-based energetic degradation function which bridges the topologic damage and energy dissipation, the topologic damage can be inserted into the framework of continuum damage mechanics, which allows this model to simulate the crack process naturally while performing nonlinear analysis without prescribed initial crack and potential propagation path. The present paper takes into account the spatial variability of the meso-scale physical parameters and employs the NMMD model to simulate the whole loading process of typical concrete specimens. The model meso-scale parameters are calibrated through the 1D modeling firstly, and the relationship between the meso-scale parameters and the meso-scale physical-geometric properties of concrete is discussed. Based on the 1D-calibrated parameters, a detailed analysis through the 2D NMMD model is performed. Further, the influence of material parameter spatial variability on the behaviors of uniaxial tensile concrete specimen and notched three-point bending beam is investigated. The work in this paper provides a meaningful reference for the calibration of meso-scale parameters in the NMMD model and the investigation on nonlinear mechanical behavior of concrete and other quasi-brittle materials under complex stress state.