Integrating wave energy converters with marine structures such as breakwaters, piles, and offshore wind turbines offers benefits in terms of wave power extraction, construction costs, and survivability. In this paper, the integration of an oscillating water column(OWC) into a vertical tubular structure is considered. The OWC chamber is enclosed by the tubular-structure with its submerged side partially open to the sea. As ocean waves propagate through the device, an air turbine installed at the top of the chamber can be driven to extract wave power. An analytical model based on potential flow theory and the eigen-function matching method is developed to solve the wave scattering and radiation problems of the device in finite water depths. Wave excitation volume flux, hydrodynamic coefficients, optimal turbine damping and power capture factor are evaluated. Upon successful validation, the model is applied to investigate the effect of the radius and finite wall thickness of the tubular-structure, the size and position of the opening on wave power extraction. We find that a thinner chamber wall thickness offers benefits to wave power extraction in terms of a broader primary band of power capture factor response, and that a broader and higher capture factor band can be achieved by increasing the height of the vertical opening.