The bending of rail due to the repeated loading from railcar wheels is a known source of rail fatigue. If rail stresses are sufficiently high, they can initiate and propagate fatigue cracks after repeated cyclic loading such that they ultimately result in rail failure. Previous analyses of stresses from wheel loads have primarily focused on track beds for which the track stiffness is assumed uniform across a length of many cross-ties. In reality, however, spatial variations of track stiffness are known to exist and are affected by many factors such as the weather. These stiffness variations can lead to stresses that are locally higher than those predicted using models based on uniform average track stiffness alone. The work presented here is focused on the influence of spatial variations of track stiffness along the rail with respect to the maximum stresses generated. A computational model of a rail on a set of crossties with a statistically varying stiffness is used to study the maximum stresses generated when the track stiffness is not spatially uniform. The mean and standard deviation of the local track stiffness are varied and the maximum stresses at various positions within the rail are examined. This computational procedure is repeated for an ensemble of local track stiffness profiles to acquire the needed statistics of the corresponding stresses. These stresses are then related to crack initiation and the expected rate of crack propagation relative to the given the statistics of the track stiffness. This work is anticipated to have application for rail maintenance and the scheduling of rail defect inspections.