This paper investigates the fluid-solid coupling problem in fractured porous elastic media. The geometry of the fractures is considered a potentially non-planar interface. The model equations are of mixed-dimensional type, where the flow equations on the \(d-1\) dimensional fracture surfaces are coupled with the d dimensional porous matrix. This paper considers a strongly compressible fluid flow model, where the density is chosen as the primary variable, in contrast to the slightly compressible model discussed by Girault et al. [5]. (Girault et al. Mathematical Models and Methods in Applied Sciences. Vol. 25, No. 4 (2015) 587–645), which takes pressure as the primary variable. We derive a thermodynamically consistent mathematical model and present its weak formulation. Energy stability is established for continuous and semi-discrete (in time) cases. The proposed model and numerical framework provide a solid foundation for simulating strongly compressible flows while maintaining thermodynamic consistency and stability.