Type 1 diabetes mellitus (T1DM) is an autoimmune disease characterized by the dysfunctional metabolism of carbohydrates, fats, and proteins caused by impaired insulin secretion and insulin resistance. This study investigated the feasibility of using point shear wave elastography (pSWE) of the pancreas by comparing the shear wave velocity (SWV) measurements of three anatomical areas in patients with T1DM and healthy volunteers. This study included 30 patients with T1DM (9 male, 21 female) and 23 healthy controls (11 men, 12 women). Two experienced certified operators performed the examinations and took the SWV measurements. The mean SWV of the entire pancreas parenchyma differed significantly between patients and controls (1.1 ± 0.29 and 0.74 ± 0.19 m/s, respectively; p ≤ 0.001). Moreover, the SWVs of the pancreatic segments were significantly different in patients and controls; the mean SWV values of the pancreas head, body, and tail (respectively) in patients vs. controls were 0.99 ± 0.36 vs. 0.76 ± 0.26 m/s (p = 0.012), 1.1 ± 0.52 vs. 0.74 ± 0.23 (p ≤ 0.001), and 1.0 ± 0.34 vs. 0.73 ± 0.28 (p ≤ 0.001). This study confirmed the feasibility of quantifying pancreas tissue stiffness with pSWE and revealed that patients with T1DM had higher pancreas tissue stiffness than controls. Further studies are required to determine the potential value of pSWE as a screening tool in patients with prediabetes.