The 2003 Tokachi-oki earthquake (M_w = 8.0) caused the severe damage to oil storage tanks by liquid sloshing, especially at Tomakomai in Hokkaido, northern part of Japan, where large liquid sloshing was excited by the long-period strong ground motions. In view of severe damage to oil storage tanks and mega earthquake threats such as Tokai, Tonankai, and Nankai earthquakes, many studies have been carried out associated with source models of huge earthquakes, S-wave velocity structural models, and simulation methods. Based on these knowledge, strong ground motions including a long-period range, from a few to over ten seconds, were predicted by several researchers for future earthquakes in the Nankai Trough region and provided to Japan Society of Civil Engineers and Architectural Institute of Japan in order to examine seismic safety of various structures such as high-rise buildings, base-isolated buildings, suspension bridges, and oil storage tanks. Since validity of predicted ground motions are hardly verified in the long-period range, further works are expected about heterogeneous source models, three-dimensional subsurface structural models, and the effects of their fluctuations on long-period ground motion characteristics.