Recently, some big reclamation projects are being pursued in offshore areas where the water depth is far beyond ten meters and there exist clay-rich soil layers whose overconsolidation ratios are not so far from unity. The present note deals with an analytical solution for the dynamic response of soil layers appearing in the offshore seabed. Referring to the result of PS-logging performed at the boring site of Senshu-oki seabed in Osaka Bay as deep as 150m, it is found that there exists a relationship between the celerity of transversal wave, v_s (m/s), and the depth of soil layers, z (m), as v_s=30z^0.5. Another informations obtained from the soil exploration also indicate that the seabed is almost normally consolidated at this site. The characteristic solution and the procedure of dynamic response analysis in such soil layers are deduced by solving the fundamental differential equation.