Fracture ballooning usually occurs in naturally fractured reservoirs and is often mistakenly regarded as an influx of formation fluid, which may lead to misdiagnosed results in costly operations. In order to treat this phenomenon and to distinguish it from conventional losses or kicks, several mechanisms and models have been developed. Among these mechanisms under which borehole ballooning in naturally fractured reservoirs take place, opening/closing of natural fractures plays a dominant role. In this study a mathematical model is developed for mud invasion through an arbitrarily inclined, deformable, rectangular fracture with a limited extension. A governing equation is derived based on equations of change and lubrication approximation theory (Reynolds's Equation). The equation is then solved numerically using finite difference method. Considering an exponential pressure-aperture deformation law and a yield-power-law fluid rheology has made this model more general and much closer to the reality than the previous ones. Describing fluid rheology with yield-power-law model makes the governing equation a versatile model because it includes various types of drilling mud rheology, i.e., Newtonian fluids, Bingham-plastic fluids, power-law, and yield-power-law rheological models. Sensitivity analysis on some parameters related to the physical properties of the fracture shows how fracture extension, aspect ratio and length, and location of wellbore can influence fracture ballooning. The proposed model can also be useful for minimizing the amount of mud loss by understanding the effect of fracture mechanical parameters on the ballooning, and for predicting rate of mud loss at different formation pressures.