The numerical density derivative approach is used to measure fluid densities around the wellbore and to generate pressure equivalent for each phase using simplified pressure-density correlation. While statistical derivative method determines fluid phase permeabilities and also average effective permeability for a given reservoir system with new empirical model. Both methods were only tested in conventional oil and gas reservoir system. This study introduces a new mathematical model for interpreting pressures behavior of a vertical well with cross form fracture in shale gas reservoir using numerical density approach. In this case, the imposed fractures can be longitudinal and transverse but symmetrical to a reference point (the wellbore). The major advantage is that it simplified the complex fracture-matrix flow equation by applying ordinary laplace transform model OLTM to formulate linear, bilinear and trilinear flow model. The model is tested for constant pressure and constant rate conditions with the generated average fluid phase pressure-densities equivalent displaying the distinctive fractures flow fingerprint. It also indicates that the dimensionless rate or pressure derivative response and distinctive flow regions are influenced by mostly fracture’s conductivities, dimensions and reservoir’s boundaries. A new flow region have been added with the first as the linear flow region which is the flow along the vertical plane parallel into the wellbore and the second as the Bilinear or Trilinear flow region which is the flow along the vertical plane parallel to the wellbore, then into the fracture after the pressure pulse reaches the upper and lower impermeable boundaries depending on the ratio of primary and secondary cross form fracture lengths and conductivities. In this paper, it has been demonstrated that for constant rate solution, the smaller the fracture aperture, the reduction in the number of flow regions to be seen.