Yamashita began to study the guitar at the age of eight with his father, Toru Yamashita. In 1972, aged eleven, he won the Kyushu Guitar Competition. Four years later, he was awarded First Prize in the All Japan Guitar Competition. In 1977, he won three important international competitions - the Ramirez in Spain, the Alessandria in Italy and Paris Radio France Competition, being the youngest winner ever recorded.
In 1978, Yamashita made his debut in Japan and, in the following year, traveled to Europe. While still in his twenties, he made his first appearances in Canada's Toronto International Guitar Festival and gave a solo recital in the Musikverein (Grosser Saal) in Vienna, he also performed in the US and UK. He gave solo recitals in concert halls around the world such as the Lincoln Center and has performed with a variety of orchestras and conductors in Europe, North America and Asia.
Yamashita's early arrangements of Pictures at an Exhibition, Stravinsky's Firebird Suite, Dvořák's New World Symphony no. 9 in E Minor, and others, broke boundaries in terms of solo guitar expression and virtuosity.