A relativistic quark model of the hadron based on the bag theory is presented. The bag equations for massless, Dirac fields with quark quantum numbers are solved in three space dimensions for the special case of a static spherical boundary. These solutions are quantized in an approximation which neglects zero-point fluctuations. The spectrum of lowlying baryon resonances is constructed. The only parameter of the model is fixed by the average mass of the $N(938)$ and $\ensuremath{\Delta}(1236)$. The gyromagnetic ratio, axial-vector charge, and charge radius of the proton are computed and found to be 2.6, 1.09, and 1.0 fm, respectively. Refinements of the quantization procedure are discussed.
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