Baranov formula in frequency domain for transient lateral vibrating piles is derived by the Fourier transform. Expressions of Winkler parameters k and c are derived by the Baranov formula. Because the rigorous expressions are complicated

they are not suitable for calculating transient lateral vibration of piles

and for this reason the simplified expressions of k and c are derived by asymptotic expansion of the Hankel function. Mobility curve and velocity one at pile head

when k and c are calculated by the rigorous expressions

are compared with those calculated by the simplified ones. Good agreement between the two results indicates that the simplified expressions are effective for transient lateral response of piles.