Quality assessment of stiffness and load-carrying capacity of composite connections is of great importance when it comes to designing timber–concrete composite structures. The new European regulation intended explicitly for timber–concrete structures has made a significant contribution to this field, considering that until today there was no adequate design standard. Due to the proposed general expressions for determining the stiffness and load-carrying capacity of composite connections made with dowel-type fasteners, which are incapable of describing most of the commonly applied fasteners, engineering, and scientific practice remained deprived of a quality assessment of the essential mechanical properties of the connection. In order to overcome this problem, this paper proposes a numerical model of the connection suitable for determining the whole load–slip curve, allowing it to estimate the stiffness and load-carrying capacity of the connection. The model was developed by considering the non-linear behavior of timber and fasteners, which is determined through simple experimental tests. For the numerical model validation, experimental tests were carried out at the level of the applied materials and on the models of the composite connection. Through numerical simulations, analysis of obtained results, and comparison with experimental values, it can be confirmed that it is possible to simulate the pronounced non-linear behavior of the timber–concrete connection using the proposed model. The estimated values of stiffness and load-carrying capacity are in agreement with the conducted experimental testing. At the same time, the deviations are much less than the ones obtained from recommendations given by the new regulation. Additionally, apart from evaluating the value and the simulation of the complete curve, it is possible to determine local effects, such as the crushing depth in timber and concrete, the fastener’s rotation, and the participation of forces in the final capacity of the connection.