A hybrid finite-element-boundary element method is adopted for the analysis of linear induction machines (LIM) in Cartesian coordinates. A mathematical boundary is defined arbitrarily in free space to enclose the system. Finite-element formulation is applied for the interior region and boundary integral formulation is applied on the boundary using the response function excited by a transverse line current. The electromagnetic field problem is solved for the magnetic vector potential, from which all performance calculations such as air gap power, propulsion force, and levitation force can be obtained. It provides an accurate analysis of the LIM in unbounded free space which can be used as a fast evaluation method to approach the proper design. The accuracy of the method is verified through experimental results in the existing literature. The comparison with finite element method is also explored.