The instances of vortex ring evolving in confined domains is observed in biological and engineering flows. The evolution of a vortex ring inside a square confinement is studied numerically using Lattice Boltzmann method. The thesis discusses the effect of Reynolds number and aspect ratio of the vortex ring on the evolution of the ring for various confinement ratios. Two domains of the flow are considered here, namely, periodic in streamwise direction and fully closed wall enclosure. The ring decay rate is found to be accelerated with the increase in the confinement ratio. The symmetry of the ring breaks due to confinement and it depends on the forward velocity or Reynolds number. The evolution of the ring is characterized by several parameters such as kinetic energy and vorticity, and the effect of wall interaction from confinement is also investigated. Preliminary studies on the effect of swirl and eccentricity are also carried out.