In many industrial applications poroelastic materials are applied as efficient noise reduction measures. This paper presents an efficient Wave Based modelling procedure to predict the absorption and transmission coefficient of infinite poroelastic materials containing a periodic grid of inclusions. As compared to standard numerical prediction schemes it offers the following advantages: (1) contrarily to Transfer Matrix Methods the layers do not need to be homogeneous, (2) contrarily to multipole methods, the inclusions do not need to be circular, (3) contrarily to element based prediction techniques, unbounded domains can easily be accounted for. Moreover, the procedure allows more easily for optimisation routines since it is a meshless and computationally more efficient technique. The Wave Based Method is an indirect Trefftz approach; it approximates the dynamic fields using a weighted sum of exact solutions of the governing differential equations. The Multi-Level Wave Based Method, which allows to describe the dynamic field of a cavity containing an inclusion, is extended in two ways: (1) Bloch-Floquet conditions are imposed on the boundaries to take into account the periodicity of the complete structure and (2) novel unbounded acoustic wave functions are presented that fulfil the acoustic Helmholtz equation, the Sommerfeld radiation condition and the Bloch-Floquet conditions. The implementation of the method is validated with the multipole method.