We investigate two algorithms for computing the Moore--Penrose and Drazin inverse of a given one-variable polynomial matrix by interpolation. These algorithms differ in the method used for constant matrices inverses computing. The first algorithm uses the Grevile's method, and the second one uses the Leverrier--Faddeev method and its generalization. These algorithms are especially useful for symbolic computation in procedural programming languages. We compare results by implementing the algorithms in the programming package MATHEMATICA and in the procedural programming languages DELPHI and C++.