A method for approximating irrational transfer functions by rational transfer functions based on the Lagrange interpolation formula is presented. The mathematical procedures required are conceptually and computationally simple. The procedure is applied to two cases, one where it is desired to approximate an irrational controller, and the other where it is desired to approximate the plant. In the latter case, it is shown that the procedure will produce a third order rational approximation with lower error than a previously reported third order approximation.