We have developed a 1D stochastic algorithm for estimating reservoir properties, based on matching large numbers of pseudo-wells to seismic angle stacks. The pseudo-wells are part deterministic and part stochastic 1D stratigraphic profiles with consistent elastic and reservoir properties. Pseudo-wells are sampled from a prior distribution defined by the geological interpretation, a rock physics model and a model for the vertical statistics that provides close control of the lithofacies proportions. A new set of pseudo-wells, typically tied to the local stratigraphy, is constructed for each seismic trace. Synthetics, derived from the pseudo-wells using extended elastic impedance, are matched to either one or two seismic angle stacks, and the best matches are selected and averaged to provide a joint estimate of reservoir properties and impedances and the associated uncertainties. The algorithm has been tested on a number of data sets and validated by blind well ties. The algorithm is 1D with no additional constraints on spatial correlation beyond that provided by the seismic data. This restricts the maximum frequency to that of the seismic; however, it makes the algorithm highly parallelizable, allowing for large data sets to be inverted in a few hours given adequate computing resources. We envisage that this inversion algorithm could form the first part of a two-step process with the output used to constrain subsequent geostatistical modeling.