A new numerical model of five uncoupled spring elements is proposed to simulate the panel-to-panel Cross-Laminated Timber (CLT) connections made of discrete fasteners. The model accurately simulates the main phenomenological effects in the translational and rotational directions of connections: asymmetrical axial gap (open/closure), in-plane and out-of-plane sliding of panels, and radial/bending stiffness/strength of fasteners. Linear/nonlinear spring elements with different constitutive material models for each phenomenological effect are considered. For instance, a modified Richard-Abbott model is used for the radial/bending hysteresis of fasteners. The model is implemented in the ANSYS software through user elements and material routines. An illustrative example under different loading conditions is elaborated to show the main capabilities of the proposed model. Finally, the model is validated with two experimental monotonic in-plane CLT slab tests, where the initial/hardening stiffness, strength capacity, and failure mechanism of both specimens are correctly predicted.