We investigate the electron ground state energy, the first excited energy and the electron density of probability within the effective-mass approximation for a finite strain elliptical wire. A magnetic field is applied perpendicular to the wire axis. The results are obtained by diagonalizing a Hamiltonian for a wire with elliptical edge. The electron levels are calculated as functions of the ellipse parameter of the wire with different values of the applied magnetic field. For increasing magnetic field the electron has its energy enhanced. The electron energy decreases as the elliptical wire size increases. The density of probability distribution in the wire with different size in the presence of a magnetic field has been calculated also. The smaller elliptical wire size can effectively draw electron deviation from the axis. Calculated ground state energy is compared with that one obtained in previous work. Key Words: energy levels, electron density of probability, magnetic field, elliptical wire I. INTRODUCTION In the past 40 years, modern growth techniques like molecular beam epitaxy, chemical vapour deposition metal organic chemical vapour deposition and advanced lithography techniques have made the realization of high quality semiconducting heterostructures possible. The peculiar optical and electronic properties of nanometric systems with quantum-confined electronic states are promising for uses in devices. Low-dimensional quantum nanostructures such as quantum wires and quantum dots have attracted considerable attention in view of their basic physics and potential device applications. 1-2 Quantum wire nanostructures can be fabricated now with monolayer precision, with dimensions of a few nanometers, free from damage due to lithographic processing by the use of all-growth fabrication processes based on epitaxial techniques. One of the most successful all-growth techniques for fabricating wires has been cleaved edge overgrowth. 3-5 In this approach, elliptical wires are created. Because of size quantization, the physical properties of charge carriers in quantum structures strictly depend on external shape of the system under investigation. Recently, considerable effort was devoted to the achievement of self-assembled quantum wires, which can be formed under certain growth conditions by solid source molecular beam epitaxy. In this case the wires are formed by the Stranski-Krastanow growth mode, in which the materials that are deposited on top of each other have a substantially different lattice parameter. Spontaneous formation of self-assembled InAs quantum wires on InP (001) substrate, having 3.2% lattice mismatch, has been recently demonstrated. 6-7 These nanostructures are promising candidates for light-emitting devices for wavelengths 1.30 µm and 1.55 µm 8-9 In the theoretical works, it is customary to assume a circular, rectangular, V-groove and T shape for quantum wire. Considerable experimental and theoretical attention has also been devoted to elliptical quantum wire and ellipsoidal quantum dot. There ...