The objective of this study is to classify lithology/fluid(LF) variables along depth profiles. The classification is done by a Bayesian inversion method to obtain the posterior probability density functions(PDFs) for the LF classes at every depth, given data in form of petrophysical variables or elastic properties. In this way we determine the most probable lithology/fluid profile. A stationary Markov chain prior model will be used to model the continuity of the LF classes a priori. The likelihood relates the LF classes to data. A statistical rock-physics forward model is used to relate the petrophysical variables to elastic attributes. This will be done for synthetic test data inspired by a North Sea sandstone reservoir and for real test data in form of a well log from the North Sea. Data for the synthetic case is either the petrophysical variables or the elastic properties. For the real data is only the elastic properties considered.