We study the behavior of Fabry-Perot micro-optical resonators based on cylindrical reflectors, optionally combined with cylindrical lenses. The core of the resonator architecture incorporates coating-free, all-silicon, Bragg reflectors of cylindrical shape. The combined effect of high reflectance and light confinement produced by the reflectors curvature allows substantial reduction of the energy loss. The proposed resonator uses curved Bragg reflectors consisting of a stack of silicon-air wall pairs constructed by micromachining. Quality factor Q ~1000 was achieved on rather large cavity length L = 210 microns, which is mainly intended to lab-on-chip analytical experiments, where enough space is required to introduce the analyte inside the resonator. We report on the behavioral analysis of such resonators through analytical modeling along with numerical simulations supported by experimental results. We demonstrate selective excitation of pure longitudinal modes, taking advantage of a proper control of mode matching involved in the process of coupling light from an optical fiber to the resonator. For the sake of comparison, insight on the behavior of Fabry-Perot cavity incorporating a Fiber-Rod-Lens is confirmed by similar numerical simulations.