We report what is to our knowledge the first accurate theoretical investigation of the electromagnetic behavior of 2-D elliptical lenses of finite wavelength-scale size. The role of internal resonances in the focal domain formation is studied. A proposal of a narrow-band receiver based on a hemielliptic lens tuned to a resonance is discussed. Possible features of such a lens-coupled receiver are stability of the resonance field with respect to the angle of arrival of incident wave and several times greater values of the peak field intensity that may potentially lead to higher sensitivity and better scanning performance. In the analysis, we use the Muller boundary integral equation (BIE) technique. This full-wave mathematically rigorous method is combined with trigonometric Galerkin discretization to result in the efficient numerical solution for an arbitrary set of the electrical, geometrical, and material parameters. Numerical results are generated for a quartz elliptical lens (ε= 3.8) with dimensions typical to mm-wave radar applications. Near field analysis, lens-focusing properties and lens frequency-dependent performance are presented.