In many countries today, cross-laminated timber (CLT) panels are increasingly being used in structural applications. CLT has many key advantages such as high strength-to-weight ratio in comparison to other common construction materials, excellent sustainability credentials, easy handling in construction, quick erection time, and good thermal and sound insulation. CLT exhibits complex behaviour; therefore, powerful theories are required to provide a better understanding of the mechanical behaviour of CLT panels and to enable their efficient and safe application in structural engineering. From that point of view, developing theoretical and numerical solutions for the analysis of CLT panels is an active research topic. A CLT panel is a laminated composite panel and, from an engineering design point of view, it can be considered as an orthotropic composite material with an elastic behaviour. Existing analytical approaches for CLT panels have limitations in applicability and accuracy. Hence, the State Space Approach (SSA) has the potential to improve the accuracy and range of applicability over these existing methods. The SSA provides theoretically accurate three-dimensional solutions that guarantee continuous transverse stress distributions across the thickness of the plates. Also, the boundary conditions and the continuity at the interfaces are satisfied (Ye, 2003). Thus, the research presented in this thesis will investigate CLT panels using the novel application of this approach. Before focusing on the specific application to CLT, the general SSA is explored for simply supported orthotropic composite plates under different types of out-of-plane loads. A new analytical solution by using the SSA for the case of a plate with three sides simply supported and one free edge under different out-of-plane loads will be developed and the derivations for the equations will be shown in detail. Note that this is the first time the SSA formulation for this particular boundary condition has been developed. For both the aforementioned and fully simply supported boundary conditions, the results obtained by using the SSA are compared with existing experimental works, various existing analytical approaches and numerical methods. To provide more knowledge and understanding of this particular application, numerical modelling of CLT using the Finite Element Method (FEM) via ABAQUS is conducted. Although the FEM is very applicable in understanding the general structural behaviour of the panel, it shows discontinuity of the transverse shear stresses at the interfaces of each ply of the CLT since, in the case of solid elements, the transverse stresses are obtained from the displacement field not from the equilibrium equations. Crucially, the SSA overcomes this problem and shows continuous stress distributions between the plies. Ultimately, this work shows that, for the boundary conditions examined, the SSA provides an accurate and efficient way to capture the structural behaviour of CLT panels subject to out-of-plane loads and can outperform some of the existing analytical methods commonly used in practice.