Background: The oculocardiac reflex (OCR) is defined as a 10–20% reduction in heart rate (HR) from the baseline value or dysrhythmia, and the oculorespiratory reflex (ORR) manifests as shallow respiratory movement and bradypnea caused by manipulation of the eye. The aim of this study was to elucidate whether the specific muscle operated on has an effect on OCR and ORR, as well as whether the depth of anesthesia influences the OCR and ORR in patients undergoing strabismus surgery with laryngeal mask airway (LMA) to maintain spontaneous respiration. Methods: The medical records of patients who underwent strabismus surgery on lateral rectus (LR) and medial rectus (MR) muscles from January 2017 to December 2017 were reviewed. For anesthesia induction, propofol was administered and the LMA was inserted. Anesthesia was maintained with sevoflurane and spontaneous respiration. Results: The incidences of OCR during LR and MR operations were not significantly different between pediatric and adult patients (29% vs 27% and 15% vs 16%, respectively, p < 0.05). The incidence of ORR, as indexed by tidal volume (TV), was higher during MR surgery than during LR surgery in pediatric patients (29.3% vs 10.1%, p < 0.05). The change in HR during muscle traction and bispectral index (BIS) showed a negative correlation in pediatric patients, but this was not statistically significant. The change in TV during muscle traction and BIS was significantly correlated, in both pediatric and adult patients (r2 = 0.034 and 0.058, respectively, p < 0.05), while the change in respiratory rate (RR) during muscle traction and BIS did not show a significant correlation in either group. Conclusions: The incidence rate of OCR did not differ between LR and MR surgeries, and the depth of anesthesia did not correlate with HR changes during muscle traction. Young age and MR surgery may be risk factors for ORR. However, MV did not decrease because of the increased RR during muscle traction. Thus, maintenance of spontaneous respiration with an LMA is safe during strabismus surgery under general anesthesia for both pediatric and adult patients.