Ulcerative colitis (UC) is an inflammatory bowel disease (IBD) that causes regions of ulceration within the interior of the colon. UC is estimated to afflict hundreds of thousands of people in the United States alone. Ultrasonic techniques can detect colitis, but have limited spatial resolution, which frequently results in underdiagnoses. Nevertheless, clinical diagnosis of colitis is still generally performed via colonoscopy. Optical techniques such as confocal microscopy and optical coherence tomography (OCT) have been proposed as higher resolution alternative imaging modalities to detect colitis. Additionally, IBD can potentially alter tissue biomechanical properties, which cannot be quantified from structural imaging alone. Elastography is a potential method to assess colon biomechanical properties to provide additional contrast for distinguishing healthy and diseased colon tissue. In this work, we induced elastic waves in ex vivo mouse colon tissue using a focused air-pulse. The elastic waves were detected using a phase-stabilized swept source optical coherence elastography system, and the wave velocity was translated into stiffness. Measurements were taken at six random positions for each sample in order to assess regional sample elasticity. The results show distinct differences ($p \lt 0.05$) in the stiffness between healthy and IBD-diseased samples, with a Young's Modulus of $10.2 \pm 3.7$ kPa and $4.9 \pm 0.3$ kPa, respectively. Dispersion analysis presents another parameter to distinguish tissue health. The high frequency components of the phase velocity dispersion curve indicate a variation between healthy and IBD colonic tissue. Our results show that OCE may be useful for detecting IBD noninvasively.