Theories used to predict the sound insulation of double-leaf cavity wall systems are usually based on the assumption that the wall is of an infinite extent. To account for the effect of the finite extent of the wall, limiting the angle of incidence, a finite radiation efficiency model or the spatial windowing method is used in order to obtain realistic predictions. However, the effects of the finite extent of the cavity are often not included. This paper presents an extension of a finite two-dimensional cavity theory to include limp panels on each side of the cavity. It is shown that the oblique incidence mass-air-mass resonance can only occur for certain frequencies and certain angles of incidence. This is the reason why the infinite extent theories under-predict the sound insulation. The results of the predicted sound insulation agree with measurements when the wall cavity is empty. To obtain agreement when the cavity is full of a porous sound absorbing material, a flow resistivity of about one-fifth of the measured value has to be used. Use of the actual flow resistivity gives sound insulation values that are 10 dB too high.