Custom mouthguards are used in various sports disciplines as a protection for teeth, temporomandibular joints, and soft tissues of the oral cavity from impact forces. The purpose of this research was to evaluate the mechanical properties of flexible polymeric 3D-printable materials and to select a material with the most favourable physical properties for making intraoral protectors. Four 3D-printable polymeric materials were selected for the evaluation: IMPRIMO LC IBT (Scheu-Dental, Iserlohn, Germany), Keyortho IBT (EnvisionTEC, Gladbeck, Germany), IBT (Formlabs, Somerville, MA, USA), and Ortho IBT (NextDent, Utrecht, Netherlands). A total of 176 samples (44 from each material) was 3D-printed using the stereolitography (SLA) technique. Tensile strength, flexural strength, notch-toughness, Shore hardness, sorption, and solubility tests were conducted. The materials were compared using a series of analyses of variance (one-way ANOVA) with Bonferroni post hoc tests. Statistical analyses were performed with the use of IBM SPSS Statistics 28.0.0 software (IBM, New York, NY, USA). Each material was assigned a score from 1 to 4 depending on the individual test results, and tests were given indexes according to the significance of the parameter in the mouthguard protective function. The number of points obtained by each material in each test was then multiplied by the test index, and the results were tabulated. The material with the highest result among the ones studied—most suitable for the application in mouthguard fabrication—was Keyortho IBT from EnvisionTEC.