Whispering gallery modes (WGMs) excitation in a cylindrical microresonator formed by a section of silica optical fiber has been studied. Evanescent light coupling into the microresonator is realized using a tapered optical fiber, fabricated by a microheater brushing technique. Several types of silica fibers with different diameters are studied as microresonators, and the influence of the resonator's diameter on the excitation of WGMs is investigated. The excitation of WGMs in a cylindrical fiber resonator were studied with changes to the tilt angle between the microcylinder and the fiber taper in the range of angles from a perpendicular position (0°) to large tilt angles (24°). The evolution of the fiber taper transmission spectrum with the change of the tilt angle results in changes in the intensity, broadening of and a blue shift in the WGM resonance spectra. Overall losses in the taper transmission spectrum decrease with the increase of the taper tilt angle from its perpendicular position, followed by a complete disappearance of the WGM resonances at large tilt angles greater than 20°.