The impact of the static friction coefficient, the initial particle orientation, and the particle height-to-diameter ratio on the bed voidage of random packings with a low tube-to-particle diameter ratio is investigated for spherical and cylindrical particles using the discrete element method. Based on the numerical results a correlation is proposed to predict the bed voidage as a function of the static friction coefficient and the tube-to-particle diameter ratio for spheres, equilateral and non-equilateral cylinders. This correlation is extended for the use of hollow cylinders.