Two popular methods for numerical Laplace inversion are used to invert some Laplace transforms arising in chemical engineering problems. These methods have been chosen as they theoretically have general applicability and are relatively simple to implement. The first method devised by Zakian and known as I(MN) approximants inverts the transform by approximating a delta function by a delta convergent sequence. The second method developed by Honig and Hirdes is a sophisticated application of the trapezoidal rule to Bromwich’s integral. In general, both methods give satisfactory results. However, the latter method is to be preferred when high accuracy is desired with a FORTRAN compiler having no more than double precision facilities. Zakian’s method is generally faster but requires quadruple or higher precision facilities for results of similar accuracy to those obtained with the method of Honig and Hirdes employing double precision. We propose a method for checking the accuracy of the results and give an extended table of values of M and N for I(MN) approximants of full grade.