This paper presents a canonical Hamiltonian model of liquid sloshing for the container coupled with spacecraft. Elliptical shape of rigid body is considered as spacecraft structure. Hamiltonian system is an important form of mechanical system. It mostly used to stabilize the potential shaping of dynamical system. Free surface movement of liquid inside the container is called sloshing. If there is uncontrolled resonance between the motion of tank and liquid-frequency inside the tank then such sloshing can be a reason of attitude disturbance or structural damage of spacecraft. Equivalent mechanical model of simple pendulum or mass attached with spring for sloshing is used by many researchers. Mass attached with spring is used as an equivalent model of sloshing to derive the mathematical equations in terms of Hamiltonian model. Analytical method of Lyapunov function with Casimir energy function is used to find the stability for spacecraft dynamics. Vertical axial rotation is taken as the major axial steady rotation for the moving rigid body.Slosh of fluid in moving objects is important for its stable movement. Vehicles on road, ships on sea, air plane motion and spacecraft all are affected by the sloshing of fuel. Such type of fluid movement can be a reason of attitude disturbance or structural damage. This is the reason why many scientists are interested to control and to minimize the effect of sloshing on the moving bodies. 1-3 Fuel dynamics is most challenging factor in microgravity environment of spacecraft and satellites. Due to fuel consumption, fill-level inside the tank of spacecraft changes and this partially filled container becomes an important driver in the dynamics of object. This can influence the moving object trajectory in three ways. First, physical properties of maneuver change by the command of pilot. Second, in low gravity the fuel flow to the thrusters is not interrupted. Third, fuel impacts on the walls of tank which is depending on the structure and frequency of fuel inside the tank. To study and control this movement, an equivalent mechanical model of simple pendulum or mass attached with spring for sloshing is used by many researchers. [4][5][6] In this article Hamiltonian system for the stability of spacecraft is used. Hamiltonian system is a dynamical system of differential equations which can be written in the form of Hamilton's equations. Such systems are usually formulated in terms of Hamiltonian vector fields on a Symplectic Poisson manifold. The transition to chaos and bifurcation for a Hamiltonian system is different from that for a dissipative system. For an integrable Hamiltonian system, the motion is quasi periodic, i.e., the motion is oscillatory but depending on more than one independent frequencies. Canonia) Corresponding author. Hamiltonian systems include harmonic oscillators (simple mass attached with spring or system of coupled linear strings), the pendulum, some special tops (Euler and Lagrange tops), and the Kepler motion of a planet around sun. A moving mass coupled with...