We evaluate the effect of excitation angles on the observation and characterization of surface wave propagations used to derive tissue's mechanical properties in optical coherence tomography (OCT)-based elastography (OCE). Air-pulse stimulation was performed at the center of the sample with excitation angles ranging from oblique (e.g., 70° or 45°) to perpendicular (0°). OCT scanning was conducted radially to record mechanical wave propagations in 360°, and the wave features (amplitude, attenuation, group and phase velocities) were calculated in the spatiotemporal or wavenumber-frequency domains. We conducted measurements on isotropic, homogeneous samples (1-1.6% agar phantoms), anisotropic samples (chicken breast), and samples with complex boundaries, coupling media, and stress conditions ( porcine cornea, intraocular pressure (IOP): 5-20 mmHg). Our findings indicate that mechanical wave velocities are less affected by excitation angles compared to displacement features, demonstrating the robustness of using mechanical waves for elasticity estimations. Agar and chicken breast sample measurements showed that all these metrics (particularly wave velocities) are relatively consistent when excitation angles are smaller than 45°. However, significant disparities were observed in the porcine cornea measurements across different excitation angles (even between 15° and 0°), particularly at high IOP levels (e.g., 20 mmHg). Our findings provide valuable insights for enhancing the accuracy of biomechanical assessments using air-pulse-based or other dynamic OCE approaches. This facilitates the refinement and clinical translation of the OCE technique and could ultimately improve diagnostic and therapeutic applications across various biomedical fields.