Inflow and outflow boundary conditions are essential for the application of computational fluid dynamics to many engineering scenarios. In this paper we present a new boundary condition implementation that enables the simulation of flow through permeable boundaries in the Lagrangian mesh-free method, smoothed particle hydrodynamics (SPH). Each permeable boundary is associated with an inflow or outflow zone outside the domain, in which particles are created or removed as required. The analytic boundary condition is applied by prescribing the appropriate variables for particles in an inflow or outflow zone, and extrapolating other variables from within the domain. Characteristic-based non-reflecting boundary conditions, described in the literature for mesh-based methods, can be implemented within this framework. Results are presented for simple one-dimensional flows, quasi-one-dimensional compressible nozzle flow, and two-dimensional flow around a cylinder at Reynolds numbers of 40 and 100 and a Mach number of 0.1. These results establish the capability of SPH to model flows through open domains, opening a broad new class of applications. Copyright (C) 2008 John Wiley & Sons, Ltd.