Human can realize flexible and skillful movements by controlling his/her musculoskeletal system and the interactive force with environments appropriately. However it still exist many uncertain biological motor characteristics in human movements even for a simple task. This paper aims to analyze and evaluate acceleration characteristics of the human hand during quick arm motion. First, the dynamic manipulability of end-point via muscle forces, called Human Muscular Mobility Ellipsoid (HMME), is newly defined. Next, the direction-dependent acceleration characteristic of the human hand motion is examined and analyzed its geometrical properties with an approximation ellipses of measured data. It is also discussed the problem that the conventional measures relative to the performance of end-point acceleration cannot represent the geometrical properties of human generated hand acceleration in good agreement with the measured data. Finally, the merits of HMME compared with the conventional measures is then demonstrated with a set of experimental results and computed results: HMME can be utilized in representing the geometric properties of human hand acceleration.