Double-walled structures separated by an acoustic cavity are widely used in many applications for sound insulation purposes. Their sound transmission loss is estimated by calculating the ratio between the incident sound power on the first wall and the radiated sound power by the second. The introduction of a poroelasic layers brings a better sound insulation against external noise. In this context, this work deals with the numerical prediction of the sound radiation from a double-walled structure with poroelastic layers. The proposed approach is based on a finite element methods for the discretization of the different solid and fluid domains of the problem. A mixed displacement-pressure variational formulation of the Biot poroelasticity equations is used to model the poroelastic domain. The structure is excited by a diffuse field represented by a superposition of plane waves with random phases and directions. The acoustic power radiated by the second wall is calculated by applying the Rayleigh integral method. The results show the importance of optimizing the position of the porous layers to maximize the sound insulation.