This study develops a novel non-orthogonal elastoplastic (NOEP) constitutive model framework for soils under steady environment conditions, which combines the characteristic stress method with a non-orthogonal plastic flow rule to comprehensively capture complex three-dimensional (3D) mechanical behaviors of soil. The framework utilizes two characteristic stress invariants to directly characterize 3D failure conditions, while the non-orthogonal plastic flow rule dynamically determines the directions of plastic strain increment. The two are conceptually independent, but their descriptions of soil properties are complementary to each other. For clays, an ellipsoidal yield function in the characteristic stress space, combined with a non-orthogonal plastic flow rule, effectively describes critical state behaviors and stress-dilatancy relationships in 3D stress space. For sands, a stress-path-independent hardening parameter in the characteristic stress space is introduced to model transition from contraction to dilation. The model requires only five parameters for clays and seven for sands, calibrated via conventional triaxial tests. Validations against experimental data for Fujinomori clay, Grundite clay, and Toyoura sand demonstrate superior predictive acapability over the Modified Cam-Clay model in predicting strength, pore pressure, and principal strain relationships under diverse intermediate principal stress coefficients (b-values) and stress paths. The framework's versatility in capturing 3D mechanical properties, stress-induced anisotropy, and stress-dilatancy behaviours highlights its potential for advanced geotechnical analysis.