The acyclic carrier method is examined. On one hand it is slightly generalized so that its scope is significantly enlarged. On the other hand the problem of implementing this method on a computer is studied. The answer is quite positive : the acyclic carrier method can be programmed in a way which is very close to the methematical formulation. In particular the various categories and functors needed in the framework can be constructed and easily handled on a machine. The relationship between the constructions and the logical foundations of mathematics are discussed too. Some examples of actual computations are described.