Several zones of graben (Memnonia, Sirenum, Icaria, Thaumasia, and Claritas Fossae) extend radially away from the Tharsis rise in the southern hemisphere of Mars for distances of up to 3000–4000 km. These graben systems are commonly interpreted to be related to regional tectonic deformation of the Tharsis rise associated with either upwelling or loading. We explore the possibility that these giant Tharsis-radial graben systems could be the surface manifestation of mantle plume-related dike intrusion complexes. Emplacement of dikes causes near-surface stresses that can produce linear graben, and lateral dike emplacement related to plumes on Earth can produce dike swarms with lengths of many hundreds to several thousands of kilometers. We develop a Mars dike emplacement model and explore its implications. We find that the properties (outcrop patterns, widths, and depths) of the extensive Tharsis-radial graben systems are consistent with an origin through near-surface deformation associated with lateral propagation of magma-filled cracks (dikes) from plumes beneath Tharsis, particularly beneath Arsia Mons and Syria Planum. Such dikes are predicted to extend through the crust and into the upper mantle and can have widths of up to several hundred meters. Analyses of summit caldera complexes on Martian volcanoes imply that the magma supply from the mantle into shallower reservoirs is episodic on Mars, and we interpret the graben systems to be large swarms of laterally emplaced giant dikes resulting from the tapping of melt from episodically rising mantle plumes in a buffered magma supply situation. The magmatic interpretation of the Tharsis-radial graben potentially removes one of the conundrums of Tharsis tectonics in which it appeared necessary to require two distinct modes of support for Tharsis in order to explain the presence of radial graben on both the elevated flanks (attributed to isostatic stresses) and outside the rise (more consistent with flexure): dikes capable of forming the observed graben can be emplaced under a wide range of stress fields, including zero stress. The fact that almost no eruptive features are associated with the graben further restricts the ranges of magma density to values between ∼3100 and 3200 kg m−3 and crustal stress to tensions less than ∼30 MPa. Eruptions from giant dikes would be more likely to occur in regions where the crust was thinner, such as the northern lowlands, providing a potential mechanism for emplacement of recently documented Early Hesperian volcanic plains (Hr) there. Dike-related graben systems represent efficient mechanisms of lateral heat transfer in the crust and near-surface environments. Lateral dike intrusions could penetrate the cryosphere and cause melting and release of groundwater, as in the Mangala Valles area, and could also drive hydrothermal circulation systems. The geometries of such dike systems will create barriers which are likely to influence regional to global groundwater flow patterns, which may help to explain the abundance of outflow channel sources in eastern Tharsis. Improved knowledge of the Martian crust and mantle density structure will help to refine this analysis and to provide estimates of the magma densities for dikes underlying specific graben.