Localized volcanic deposits along the linear rille Rima Parry V are evidence for the presence of near-surface magma and are interpreted to be the result of degassing and minor eruptions subsequent to magma emplacement at shallow depth. Theoretical analyses, together with the observed style of emplacement of lunar mare volcanic deposits, strongly suggest that mare volcanic eruptions are fed by vertical dikes from source regions at the base of the crust or deeper in the lunar mantle. Some dikes intrude into the lower crust, while others penetrate to the surface and are the sources for voluminous outpourings of lava. Still others stall near the surface generating an extensional stress field above the dike top. We investigate the hypothesis that some lunar linear rilles (graben) such as Rima Parry V are the near-surface manifestations of dikes intruded to shallow depths and that they from simultaneously with dike emplacement. For two examples (Rima Parry V and Rima Sirsalis) the geometry of the faults implies dike widths (150 and 600 m) and depths to the dike tops ( 650 and 2400 m) that are consistent with other theoretical and observational data on lunar dike geometry. For the shallower of the two dikes (Rima Parry V), degassing and extrusion have produced pyroclastic cones and related deposits along the central part of the graben.