This paper derives and validates an analytical model for acoustic boundary conditions on a can-annular gas turbine combustion system, composed of discrete cans connected to an open annulus upstream of a turbine. The analytical model takes one empirical parameter: a connection impedance between adjacent cans. This impedance is extracted from time-marching computations of two-can sectors of representative combustors. The computations show that reactance follows the Rayleigh conductivity, while resistance takes a value of order 0.1 as a weak function of geometry. With a calibrated value of acoustic resistance, the analytical model reproduces can-to-can transfer functions predicted by full-annulus computations to within 0.03 magnitude at compact frequencies. Varying the combustor–turbine gap length, both model and computations exhibit a minimum in reflected energy, which drops by 63% compared to the datum gap. A parametric study yields a design guideline for gap length at the minimum reflected energy, allowing the designer to maximise transmission from the combustion system and reduce damping requirements.