In the long‐wavelength limit, the current distribution in a thin‐film superconducting strip transmission line can be described by an inhomogeneous Fredholm equation of the second kind. By considering a fluxoid conservation derivation of this equation, physical insight into the structure of the kernel follows naturally. An approximate analytic solution to the integral equation is derived for a specified range of geometrical parameters commonly encountered in practice. The solution is obtained by making use of the Liouville—Neumann method of successive iterations and approximating the resulting series by a series involving powers of a defined coupling factor. It is shown that the critical current of the thin‐film superconducting strip transmission line, based on the calculations in the paper and a critical‐current‐density hypothesis, is underestimated by less than 10%.