Background and Objectives: Supraglottic airway devices (SADs) are known to be useful in eliminating the drawbacks of laryngoscopy and tracheal intubation, especially ocular pressure and stress responses. The ultrasonographic measurement of optic nerve sheath diameter (ONSD) reflects increases in intracranial pressure (ICP). In our study, we aimed to compare the effects of SADs on hemodynamic response and ONSD. Materials and Methods: Our prospective study included 90 ASA I–II patients over the age of 18 who did not have a history of difficult intubation or ophthalmic pathology. The patients were randomly divided into three groups based on the laryngeal mask airway (LMA) devices used: ProSeal LMA (pLMA, n = 30), LMA Supreme (sLMA, n = 30), and I-gel (n = 30). The bilateral ONSD measurements and hemodynamic data of the patients who underwent standard anesthesia induction and monitoring were recorded before induction (T0) and 1 min (T1), 5 min (T5), and 10 min (T10) after SAD placement. Results: At all measurement times, the hemodynamic responses and ONSD values of the groups were similar. In all three groups, intergroup hemodynamic changes at T0 and T1 were similar and higher than those at other times of measurement (p < 0.001). The ONSD values of all groups increased at T1, and they tended to return to baseline values afterward (p < 0.001). Conclusions: We concluded that all three SADs could be used safely because they preserved both hemodynamic stability and ONSD changes in their placement processes, and they did not cause elevations in ONSD to an extent that would lead to increased ICP.