The fundamental solution of the linear Boltzmann equation in the two‐dimensional steady case is presented. The linear Boltzmann equation governs the perturbed distribution functionfin a steady flow over a point source. The point source is represented in the equation by a singular inhomogeneous term involving a delta function. The fundamental solution is split into three parts,f = f&dgr;+ fa+ fb. Bothf&dgr;andfaare explicit. They are singular at the origin and decay exponentially for large r. The ``remainder''fb, which satisfies an inhomogeneous linear Boltzmann equation, is bounded at the origin and behaves fluid‐dynamically like a macroscopic flow for larger. At smallr, the series expansion offbconsists of terms of integral powers ofrand integral powers ofrmultiplied by lnr, with the zeroth power ofrbeing the leading term. At intermediate and larger, fbis expressed in terms of the Euler fluid components.