Abstract: Tire turn slip models in non steady state (NSS) conditions were given according to mathematical relations of transfer functions with different lateral inputs and the NSS tire cornering models based on the carcass string theory. The function E0 in the presented models is transformed to Taylor series and partial polynomials were intercepted effectively. Then tire turn slip models in steady state conditions based on the carcass string theory were derived. Finally the non dimensional turn slip models in NSS conditions were simplified as rational fractions in general forms. The derived models can be applied to dynamics analysis and steering performances studies of tractors and automobiles.