Elastic timber gridshells are lightweight structures whose stiffness is highly dependent on multiple factors, such as boundary conditions and the semi-rigidity and eccentricity of the joints. Their structural analysis requires calibrated numerical models that incorporate all aspects influencing stiffness. Unfortunately, very little research on experimentally verified numerical models can be found. This paper focuses on the structural behaviour of a novel concept of triaxial elastic long-gridshells supported only on their short sides, called by the authors TEL-gridshells. First, the most relevant details of the construction process and the load test of a full-scale laboratory prototype are presented. Then, two finite element models for structural analysis and form-finding are proposed. Both are based on the modelling of the joints using a series of aligned couplings that allow the integration of the actual joint eccentricity and the interlayer slip by means of springs in all shear planes. The first model replicates the geometry of the prototype built from experimental measurements, focusing on stiffness calibration. The results of the load test are used to verify the proposed model and to analyse the most influential aspects on the stiffness of the structure. The second is a form-finding model that reproduces the construction process of the laboratory prototype, focusing on the residual stresses generated during the deformation process of the structural elements. From the numerical results, the structural behaviour of the prototype is discussed and some of the main aspects to be considered in the design and structural analysis of TEL-gridshells are established.