In recent years, the numerical Laplace transformation of sampled data has proven to be useful for well-test analysis applications. However, the success of this approach is highly dependent on the algorithms used to transform sampled data into Laplace space and to perform the numerical inversion. We present new algorithms to accurately transform sampled data into Laplace space and to minimize "tail effects" resulting from the extrapolation of tabulated data. The algorithms presented can be applied to generate accurate pressure-derivative data in the time domain. We show that performing curve-fitting (without inversion) in Laplace space with the algorithms presented is computationally more efficient than performing it in the time domain. Applications of the algorithms to convolution, deconvolution, and parameter estimation in Laplace space are also presented. Both synthetic and field examples are considered to illustrate the applicability of the proposed algorithms.