The authors define the class of polyhedral risk measures as optimal values of certain linear stochastic programs with recourse where the arguments appear on the right-hand sides of the dynamic constraints. They provide conditions implying that polyhedral risk measures are coherent and consistent with second order stochastic dominance. For the one-period case it has been shown that well-known risk measures are contained in the class of polyhedral risk measures introduced: Conditional-Value- at Risk/quantile dispersion, and expected loss. For the multiperiod case, five polyhedral (coherent) risk measures are suggested. In the last section, the authors shown that several properties of expectation - based stochastic programs remain valid for stochastic programs with polyhedral risk measures as objective (or, alternatively, with an objective consisting of a linear combination of an expectation and a polyhedral risk measure). In particular, they present stability results for two-stage stochastic programs with polyhedral risk measures and show that dual decomposition structures are maintained.