Periodic structures have been extensively investigated in the field of acoustics and vibrations, focusing different applications, such as acoustic barriers, cloaking devices or wave guiding systems. Different methods have been used for this purpose, including numerical and analytical approaches. A recent work has proposed the use of a meshfree formulation based on the Method of Fundamental Solutions (MFS) to tackle such problems in an infinite environment, defining fundamental solutions that may be used both in 2D and in 3D problems. In that work, the authors address the case of rigid scatterers in a 3D scenario, simulating a sonic crystal noise barrier [1]. Later, the authors extended the method for the case of scatterers with an absorbing layer made of porous material in a 2D environment [2]. In another earlier work, the case of an acoustic medium hosting a non-homogeneous inclusion has been addressed using a coupling between the Boundary Element Method (for the homogeneous host) and Kansa’s method (for the inclusion) [3]. The present paper extends the previous works by proposing a general strategy to simulate infinite periodic media with multiple inclusions with non-homogeneous properties. The host propagation medium is assumed to be homogeneous, and hosting a set of scatterers that are periodically repeated along one direction, but exhibiting acoustic properties that are variable in space. The proposed strategy addresses the problem using analytical solutions for the non-homogeneous inclusions, and the MFS, together with periodic fundamental solutions, to simulate the homogeneous part of the domain. The method is validated against Finite Element and Finite Difference (time domain) models, and an application example is given to illustrate its applicability. The proposed strategy can be quite efficient, accurate and elegant.