Examples and recorded data are used to demonstrate the need for probabilistic models in mechanics, introduce some probabilistic concepts, and formulate stochastic problems. A level-cut Poisson field is presented to show that two-phase microstructures can be represented accurately and efficiently by probabilistic models. Size effect, relationship between global and local material properties, and effective material characteristics are examined by analytical, Monte Carlo, and finite element methods. An extension is presented for the classical Galerkin method to solve equilibrium problems for physical systems with uncertain parameters, that is, systems described by differential equations with random coefficients. The stochastic Galerkin method is applied to analyze a plate on Winkler support with uncertain mechanical properties.