This thesis presents the development and application of a numerical inverse and forward model of stratigraphy applied to shallow-marine wave-dominated sedimentary systems. The approach links a 'process-based' forward model of stratigraphy (i.e. BARSIM, developed by J.E.A. Storms, University of Delft) to a fully non-linear stochastic inverse scheme. The inverse problem has been formulated using a Bayesian framework in order to sample the full range of uncertainty and explicitly build in prior knowledge. The methodology combines Reversible Jump Markov chain Monte Carlo and Simulated Tempering algorithms which are able to deal with variable dimensional inverse problems and multi-modal posterior probability distributions, respectively. The numerical scheme requires the construction of a likelihood function to quantify the agreement between simulated and observed data (e.g. sediment ages and thicknesses, grain-size distributions). Prior to real case study applications, the method has been successfully validated on different scenarios built from synthetic data, in which the impact of data distribution, quantity and quality on the uncertainty of the inferred environmental parameters were investigated. The numerical scheme has then been applied to two case studies: the outcrop-constrained Lower Cretaceous 'Standardville' parasequence of the Aberdeen Member of the Blackhawk Formation (Boock Cliffs, Utah, U.S.A.) and the Emsian sub-surface data of South Algeria. The inverse modelling scheme successfully reproduced stratigraphic architecture in both cases, within the constraints of the input data quality. The inferences of the relative sea level, sediment supply and wave regime histories contribute to the understanding of mechanisms that produced the observed stratigraphy. Of equal importance, the inverse results allowed complete characterisation of uncertainties in these forcing parameters and in the stratigraphic architecture developed in between data constraints. These results suggest that the inverse model may ultimately provide a process-based geological complement to standard geostatistical tools for the static characterization of hydrocarbon reservoirs.