This paper presents a wave and finite element method for predicting the sound transmission loss of double-leaf walls comprising panels of arbitrary complexity separated by a cavity which can contain air or an insulating material. The method is verified against analytical models and validated against a number of different experimental measurements. The method is then used to investigate the effect of various parameters on the sound transmission performance of a double-leaf cross-laminated timber (CLT) wall construction. Parameters investigated include the flow resistivity of the insulating layer separating the wall panels and the effect of panel thickness and orientation. The effect of a neoprene rubber layer in between the CLT panels is also investigated.