Tashiro graduated from Mechanical Engineering Course of Meiji.
He entered Mitsui Bussan Company and served successively at branch offices at Moji, New York, Tokyo, London and Nagoya. In 1936 Shigeki became director of Toyo Rayon Company, then managing director (1942) and finally president (1945).
Tashiro was appointed vice-chairman of Japan Chemical Fiber Association in 1948 and chairman of Toyo Rayon Company in 1950. He also served as chairman of Japan Chemical Fiber Association.