This work proposes a hybrid modelling technique for efficient analysis of poroelastic materials, which are widely used for noise reduction in acoustic problems. By combining the finite element method and the wave based method in a direct manner, the proposed hybrid technique maximises the advantages and compensates the drawbacks of both numerical methods. The considered poroelastic domain described by Biot’s theory is divided into two groups of domains according to their geometrical characteristics and boundary conditions. The group with complex geometries and/or boundary conditions leading to singularities is discretised into a large number of small finite elements. The other group consisting of large, geometrically moderate poroelastic domains is partitioned into wave based subdomains where the field variables are expanded with analytical poroelastic wave functions. Both groups modelled by the finite element method and the wave based method, respectively, are combined in a hybrid framework in this work to ensure their interacting dynamic behaviours. The properties of the hybrid model are investigated and are compared to existing modelling methods for some numerical examples. The proposed direct hybrid modelling technique provides stable predictions and exhibits fast convergence performances for the analysis of poroelastic materials, especially when singularities arise in the poroelastic domain. 
A direct hybrid finite element–wave based modelling technique for efficient analysis of poroelastic materials in steady-state acoustic problems