Tarim Basin newly discovered the fault-karst carbonate reservoirs, which are formed by the large-scale tectonic fault activities and multiple-stage karstification. Four kinds of mediums coexist in the reservoirs, including the large cave, vug, tectonic fracture and matrix. The tectonic fractures interconnect with large caves in series to form the vertical beads-on-string structure, which is the most common connection pattern in reservoirs. To provide a well test method for evaluating this type of structure, this work firstly presents a multi-fracture-region multi-cave-region series connection physical model by simplifying vertical beads-on-string structure. We consider four kinds of mediums in the proposed physical model, including large caves, small vugs, high-angle tectonic fracture and rock matrix. The fracture regions mainly contain fracture, vug and matrix mediums. The cave regions contain cave medium. The corresponding mathematical model is also developed, in which the flow in fracture regions obeys the Darcy’s law, while the flow in cave regions is assumed to obey free flow. Furthermore, the gravity is taken into account because the flow is along the vertical direction. Then the typical flow regimes are analyzed and sensitivity analysis is conducted on crucial parameters. Results indicate that (a) the typical feature of vertical beads-on-string structure on type curves is that the cave storage regimes and linear flow regimes alternately appear; (b) the type curves will exhibit the cave storage regimes with unit-slope pressure derivative for the existence of large caves, which is different from the inter-porosity flow regimes for the existence of the vugs (slope ≠ 1); (c) the gravity effect could lead to unit-slope pressure and pressure derivative curves, which can be regarded as closed boundary in a peculiar sense; (d) gravity effect is difficult to be observed from well test curves with about 2-weeks test duration in real application. Finally, two cases from Shunbei Oilfield are interpreted to illustrate the practicability and feasibility of proposed method.