On April 25, 2015, a Mw 7.8 earthquake struck the Gorkha district of Kathmandu, Nepal. In Patan, vibrational characteristics of a 300-year-old two-story masonry building near Patan Durbar Square had been measured prior the Gorkha earthquake. In the inspection of the building after the Gorkha earthquake, several new cracks were found. The vibrational characteristics of the building were measured again, and it was found that the natural frequencies after the earthquake were smaller than those before the earthquake, indicating the reduction of the stiffness. Finite element models of the structure representing pre- and post-earthquake conditions are established so that the natural frequencies match the pre- and post-earthquake measurements and the structural damage is identified based on the stiffness reduction. Finally, the dynamic analysis of the finite element model of the building in the pre-earthquake condition using the observed ground motion record during the Gorkha earthquake as the input is conducted, and the structural response of the building during the Gorkha earthquake is discussed.