In this paper, we find the range of the pulling rate for which the system of differential equations, which governs the evolution of the crystal radius r and the meniscus height It in the case of silicon filaments grown from the melt in a vacuum by EFG method, has asymptotically stable steady states. Computation is made in a nonlinear model in two cases: the meniscus weight is ignored (H-1); the meniscus weight is considered (H-2), respectively. Computation is made for a die of radius r(0) = 20 (cm x 10(-2)). In the case (H-1) we find that the computed pulling rate range is 0.001-10.3 (cm x 10(-2))/s. For the pulling rate nu in this range the computed radius of the filament is in the range 10.095-19.357 (cm x 10(-2)) and the meniscus height is in the range 2.508-11.240 (cm x 10(-2)). In the case (H-2) we find that the computed pulling rate range is 0.001-6.18 (cm x 10(-2))/s. For the pulling rate in this range the computed radius of the filament is in the range 11.841-19.096 (cm x 10(-2)) and the meniscus height is in the range 2.5-5.5 (cm x 10(-2)). We give also model based simulation of the evolution of the crystal radius and meniscus height, when during the growth the pulling rate changes.