Fundamental period has been recently proposed to be an alternative to time‐averaged shear‐wave velocity to 30 m () and used as a proxy for site amplification in recent ground‐motion prediction equations. In this study, we propose a simple approach to construct continuous‐variation velocity models and present analytical‐numerical solutions to the fundamental period for the following three cases: (a) shear‐wave velocity increasing or decreasing linearly with depth, (b) shear‐wave velocity increasing as a power of depth, and (c) shear modulus increasing or decreasing linearly with depth. Eight practicable methods of estimating the period from shear‐wave velocity profile are also developed and discussed. The accuracy of the eight methods is evaluated by comparing the estimated values with the analytical solutions and empirical results. The results show that the linear velocity model method has high correlation coefficient and low standard deviation among the eight approximate methods for both the comparison between estimated and analytical periods and that between the estimated and empirical periods. In addition, we find that there is a significant improvement in the accuracy after modifying four times the total travel time (previous solution) as times the total travel time (proposed solution) to give a preliminary estimation of fundamental period for profiles with at least two layers.