Cerenkov radiation is generated in optical fibers immersed in radiation fields and can interfere with signal transmission. We develop a theory for predicting the intensity of Cerenkov radiation generated within the core of a multimode optical fiber by using a ray optic approach and use it to make predictions of the intensity of radiation transmitted down the fiber in propagating modes. The intensity transmitted down the fiber is found to be dominated by bound rays with a contribution from tunneling rays. It is confirmed that for relativistic particles the intensity of the radiation that is transmitted along the fiber is a function of the angle between the particle beam and the fiber axis. The angle of peak intensity is found to be a function of the fiber refractive index difference as well as the core refractive index, with larger refractive index differences shifting the peak significantly toward lower angles. The angular range of the distribution is also significantly increased in both directions by increasing the fiber refractive index difference. The intensity of the radiation is found to be proportional to the cube of the fiber core radius in addition to its dependence on refractive index difference. As the particle energy is reduced into the nonrelativistic range the entire distribution is shifted toward lower angles. Recommendations on minimizing the quantity of Cerenkov light transmitted in the fiber optic system in a radiation field are given.