The structure and mechanism for maintenance of the Great Plains squall line thunderstorm are studied through formulation of a two-dimensional, time-dependent numerical model. The environmental conditions known to be favorable for squall line development and maintenance include a convectively unstable air mass whose motion is characterized by strong vertical shear of the horizontal wind. These conditions are used to specify an environment in an x-z plane upon which a disturbance is superimposed. The appropriate physical equations are integrated forward in time to study changes in the motion, thermal and moisture fields in and around the squall line thunderstorm. The vertical shear of the horizontal environmental wind is varied from one experiment to another with the result that broader and longer lasting cloud circulations occur in the stronger shear cases. Specific areas where three-dimensional effects must be important are discussed from an examination of variable fields during periods when the system undergoes a lessening in intensity. It is found that the system, rather than reaching a quasi-steady state, undergoes a series of developments (three or four during a 100-min period) as measured by the time variation of maximum updraft speed, downdraft speed, and rainwater mixing ratio. However, the system structure during the intense stage of each development is basically the same as that during the other developments, and strongly resembles the structure envisaged in qualitative physical models suggested in the past: 1) the updraft and downdraft exist side by side, the updraft possessing an upshear tilt from the vertical through the lower half of the troposphere; 2) rain produced in the updraft falls into the downdraft, strengthening or maintaining the downdraft due to its own weight and through negative buoyancy produced by evaporation; and 3) maintenance of the downdraft results in a strongly convergent region in lower levels downshear from the system and a tendency toward updraft maintenance or redevelopment. The implication is that the squall line thunderstorm, once initiated, maintains itself by interaction with its synoptic environment as long as it remains within an environment containing convectively unstable air whose motion is characterized by moderate-to-strong vertical shear.