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In this study, extensive research has been carried out to determine the optimum geometry resulting in the highest sensitivity for the tapered fibre-optic sensors in a broad geometrical range. A staircase concatenation method was introduced to investigate the effect of the taper angle and diameter on the sensor’s sensitivity. The results show that the sensor’s sensitivity increases by reducing the taper diameter. Moreover, the effect of the tapering angle on the sensitivity has an optimum point. As a result, there is an optimum taper curvature for exponential-linear profiles, which results in the highest sensitivity. Indeed, it was revealed that the sensitivity changes versus taper diameter and angle could be justified considering the coupled power to different modes of the tapered fibre as well as the ratio of the power outside the fibre taper to the total power for different modes.