Basedonanincompressiblemodel,byusingthelargestaintheory,thecontactofarubberwedgewitharigidnotchisanalyzedbytheasymptoticmethod.Theproblemistreatedasasymmetriccase,andthecontactsurfaceissmooth.Thestressandstrainfieldneartheapexoftherubberwedgeisshowntobesingular,andtheangulardistributionsofstressandstrainareobtained.Twoimportantparameterstandtareintroducedtoattaintheconclusions.TheresultshowsthatthesingularexponentorderofstressfieldisInr.