Three-dimensional (3D) concrete printing presents significant challenges in accurately modeling mechanical behavior due to the anisotropy induced by layer-by-layer deposition and variability in inter-filament bonding. This study introduces a hierarchical Bayesian framework for selecting and calibrating constitutive models in 3D-printed cementitious materials. Three candidate models—parabolic (Model 1), Carreira–Chu (Model 2), and plastic-damage (Model 3)—were assessed using uniaxial compression data from (i) soil–cement pastes with calcium carbonate additions (0–10%), (ii) cast and 3D-printed mortars, and (iii) 3D-printed concrete tested under perpendicular and parallel loading orientations. Bayesian inference combined with information criteria (Watanabe–Akaike Information Criterion and leave-one-out cross-validation) enabled objective model selection and uncertainty quantification. The Carreira–Chu model consistently outperformed alternatives for homogeneous systems (soil–cement and mortars), while the plastic-damage model best represented anisotropic responses in printed concrete loaded parallel to the deposition direction. Experimental findings indicate a 44% decrease in elastic modulus with 10% calcium carbonate, a 9.1% increase in compressive strength for printed versus cast mortars (8.36 vs. 7.66 MPa), and a 21% strength gain in concrete loaded parallel versus perpendicular to the deposition direction, despite a 40% reduction in stiffness. The proposed hierarchical Bayesian approach provides probabilistic estimates of constitutive parameters (compressive strength, elastic modulus, and characteristic strain) and data-driven guidance for selecting suitable models for additive manufacturing of cementitious materials, enhancing the reliability of structural simulations of 3D-printed elements.