We present results from numerical MHD simulations of the emergence of twisted magnetic flux tubes from below the photosphere into the corona. The aim is to study the influence of the field line twist on the emergence process. In almost all previous studies of the emergence of flux tubes, very strong twist (more than one rotation around the buoyant region of the initial tube) was imposed. Observations of flux emergence, however, suggest that flux tubes emerging into the solar atmosphere carry lesser twist. By varying the amount of twist in the initial tube, we have carried out a parameter study with particular emphasis on the weakly twisted regime. We found the followings. (1) In weak twist case, tube fragments once around the photosphere, and emerging motion is rapidly suppressed. Then the tube expands to horizontal direction. As time goes on, emergence starts again. (2) In weak twist case, at the photosphere the magnetic tension force, which keeps tube coherent, is weak so it expands more largely than strong twist case. So magnetic fields strength in flux tube is weaker than that of strong twist case because it expands more largely. As a result of this, buoyancy force becomes weak and emerging motion is rapidly decelerated. Then expansion to the horizontal direction drastically occurs.