We report the fabrication and modeling of single-mode tapered optical fiber sensors. The fabrication technique consist of stretching a section of fiber with an oscillating flame torch. Such a process allows controllable fabrication of lossless tapered fibers with a uniform waist. The sensor transmittance is modeled with a simple ray optics approach. In the model, all the taper parameters are taken into account. Our results indicate that sensor sensitivity can be adjusted with the taper waist diameter. As an example a gold-coated tapered fiber is theoretically and experimentally analyzed.