The fracture-cavity carbonate reservoir has large scale and discontinuous medium

and its main reservoir space is composed of fractures and caverns. Many wells are independent fractured-cavity systems

and most of them connect macrofractures to the wellbore. These wells are separate fracture-cavity cells which connect with one or two big cavities in series by fracture network

so the actual flow process of the reservoir does not match the result obtained by adopting traditional continuum theory. An analytical mathematic model is presented by considering the fracture network between well-cavity and cavity-cavity as one dimensional linear fracture

and other fracture communication flow exist in the periphery of the cavity（away from wellbore）. Accordingly

the linear-in-series well test mathematic model with fracture connecting two cavity systems is established

and the model introduces the conception of transient flow and channeling flow of multiple media. The Transient conduction principle and Laplace transform are used to solve the mathematical model

and the dimensionless bottom hole pressure type curves are plotted in real space by using the improved Stehfest numerical inversion. The analysis of the sensitivity of cave parameters shows that the model can correctly reflect the relation between flow control factor and geological factor. Application examples indicate that this model can correctly explain wellbore storage factor

skin effect

the permeability of fracture system and cavity system

and the geometric parameters of fracture and cavity.