Purpose: The aim of the present study is to calculate Concavity Shape Index (CSI) in patients with POAG and exfoliative glaucoma (XFG) and correlate CSI with the severity of glaucoma, comparing to control and ocular hypertension (OHT) patients. Methods: This was a cross‑sectional study with 146 eyes/146 subjects: 37 healthy eyes, 23 eyes with OHT and 86 glaucoma eyes (70 with POAG, 16 with XFG). The severity of glaucoma was scored with the Glaucoma Staging System 2 (GSS2). Corvis ST® was used to calculate CSI. Results: Central corneal thickness (CCT) was significantly thinner in POAG (526 ± 40.0 µm) and XFG (520 ± 38.2 µm) than control group (553 ± 28.8 µm). CSI had no significant differences between the groups. XFG had a higher mean of GSS 2 (2.42 ± 1.38) than POAG (1.87 ± 1.55) and OHT (1.87 ± 1.55). OHT had a significantly less deformable cornea than: control (higher A1 length, lower A1 velocity, higher A2 velocity), POAG (higher A1 length, lower A1 velocity, lower deflection amplitude at highest concavity), and XFG group (lower A1 velocity, lower deflection amplitude at highest concavity), which was independent of age and CCT. No significant correlation was found between GSS 2 and CSI. Discussion: OHT patients had stiffer corneas (less deformed by the air puff) when compared to control, POAG or XFG patients. A less deformable cornea could potentially be related to a more resistant LC/peripapillary sclera. As such, this would result in a lesser optic nerve susceptibility to IOP damage.