Abstract : Depending on the application context, many different ways of modelling resource sharing situations have been proposed. Dijkstra's Dining Philosophers Problem is one of the first systematic attempts in the area. It was then generalized by Chandy and Misra who proposed the Drinking Philosophers Problem. We consider Markovian versions of these situations. The aim is to analyse the performances of the underlying systems through their behaviour at equilibrium. This study fits into the context of Markov fields on graphs and some general material on Markov properties is presented. New Markovian models for resource sharing are introduced. They can be viewed as interacting particle systems. Mathematical techniques of treatment such as reversibility and stochastic comparison techniques are proposed for these models. For finite systems, explicit calculations of measures at equilibrium are given. Systems increasing in size and complexity can be approximated by infinite systems. For such systems on graphs built from a tree, we show that phase transition phenomena may occur.