The work in this thesis is directed towards the measurement and prediction of the shape of the flow channel in granular solids as they discharge from flat-bottomed silos. It is widely believed that the flow pattern affects the pressure distribution against the walls and so also the stresses in the silo structure. Thus, a reliable means of predicting the shape of the flow channel has important design implications. Kinematic analysis is used as the basis for the theoretical work. The governing partial differential equation contains one unknown empirical parameter: the kinematic parameter. Finite element formulations are developed and implemented to solve for the steady-state vertical velocity field in flowing granular solids for a range of conjectured kinematic parameters. The formulations are applied to the analysis of flow from flat-bottomed silos with planar or axisymmetric geometries. Criteria are proposed to define the boundary between flowing and near-stationary solid. The flexibility of the finite element method allows many original kinematic analyses to be carried out e.g the analysis of silos with more than one outlet; the analysis of planar silos with eccentrically-positioned orifices; the analysis of the effect of a spatially-varying kinematic parameter and the modelling of the top surface displacement are all claimed to be original. Experiments are carried out in a half-cylindrical flat-bottomed silo. A rigid transparent sheet is used to form the front wall. The bisection of the flow in this way allows direct observation of flow mechanics to be made and the shape of the flow channel boundary can also be traced. Two solids are tested: a rough, frictional solid (sand) and a smooth, free-flowing solid (polypropylene pellets).