Elastic gridshells hold immense potential for deployable space structures, soft robotics, and adaptive architectures. However, predicting their mechanics is hindered by the computational complexity of discrete models and the critical coupling between joint torsion and rod bending. To address this, we develop a computational continuum framework based on a second-gradient constitutive model, which homogenizes the discrete gridshell into an anisotropic continuous shell under finite deformation. This framework unifies the coupled effects of joint torsional deformation and higher-order bending deformations of rods into a second-gradient constitutive model. The resulting geometrically nonlinear governing equations are solved via a tailored absolute nodal coordinate formulation, designed to handle the kinematic constraints and finite rotations inherent in the system. The proposed framework reveal a governing dimensionless parameter D 2k R2 6 EI k        , which integrates rod density ρ, joint stiffness kγ , Young’s modulus E, cross-sectional moment of inertia I, and characteristic dimension R into a single parameter. This parameter uniquely dictates the deformation response of elastic gridshells in the absence of local buckling. Utilizing this parameter, high-density gridshells can be equivalently reduced to low-density configurations without changing mechanical behavior, thereby significantly reducing manufacturing and computational costs. As an application, we investigate the snap-through instability of hemispherical elastic gridshells under concentrated loading. Results reveal that the emergence and suppression of snap-through instability stem from competitive energy conversion between normal bending energy and joint torsional energy, with a critical dimensionless parameter value of D=2.45 demarcating the instability phase boundary. The proposed continuum theory and computational approach not only accelerate gridshell design processes but also unveil the physical essence of gridshell mechanics, advancing the development of deployable gridshell structures.