A new approach is presented for handling problems involving radioactive decay, buildup, and mass transfer. This method uses recursion relations for computing the exponential terms that makes the computation fast and efficient. The concepts of a path specific probability function and a cumulative transfer probability function are introduced and used in developing a general equation. This general equation permits branching from a parent to any daughter nuclide further down the decay chain and also mass transfer to other compartments linked by first-order transfer rate constants. Backward branching or feedback mechanisms, however, are not permitted. Treatment for problems involving singularities is also presented. The method has been found to be useful for many practical applications such as fission product buildup in nuclear reactor cores and releases from reactor plants.