Dynamic characteristics of small-scale magnetic elements in the quiet Sun are investigated using a statistical analysis of Doppler shifts and asymmetry of V profiles of the Fe I 630.25 nm line calculated with nonstationary magnetohydrodynamic models. Distribution of vertical velocities was obtained and their correlation with the main characteristics of magnetic field was found. On the average, the downflows predominate with an average velocity of 0.5 km/s within magnetic elements. In strong magnetic tubes the average velocities are equal to 3 km/s and the maximum velocities are as high as 8—9 km/s. In weak diffuse magnetic fields upflows predominate with an average velocity of 0.5 km/s and a maximum velocity of 3 km/s. The profiles calculated with high spatial resolution (35 km) have an average value of amplitude and area asymmetries close to zero (-1 %). For weaker V amplitudes the scatter of asymmetry is ±70 %, and for stronger ones it is ±10 %. It was found that the spatial averaging of profiles influences the amplitude asymmetry more than the area asymmetry. This is a reason of the observed effect of excess of amplitude asymmetry over area asymmetry. A weak correlation between the asymmetry of V profiles and the velocity is found. Upflows cause, on the average, a negative asymmetry and downflows a positive one. Center-to-limb variations of velocities were found in magnetic elements. The average velocity increases sharply up to 2 km/s, beginning from cosθ = 0.9, and then it varies weakly, approaching the limb. Velocity oscillations are investigated, and their power peaks in 5 and 3 minute bands are found. The non-linear character of velocity oscillations are caused by field strength fluctuations. The Doppler shifts and asymmetry parameters obtained for spatially averaged V profiles are consistent with the results of FTS-observations as well as with other observations made with high spatial resolution.