The iterative Monte Carlo (IMC) method is applied to a number of one-dimensional plasma flow problems, which encompass a wide range of conditions typical of those present in the boundary of magnetic fusion devices. The kinetic IMC method of solving plasma how to a surface consists of launching and following particles within a grid of 'bins' into which weights are left according to the time a particle spends within a bin. The density and potential distributions within the plasma are iterated until the final solution is arrived at. The IMC results are compared with analytical treatments of these problems and, in general, good agreement is obtained.