Tension in the yarn and its oscillations during the over-end unwinding of the yarn from stationary packages depend on the unwinding speed, the shape and the winding type of the package, the air drag coefficient, and also the coefficient of friction between the yarn and the package. The yarn does not leave the surface package immediately at the unwinding point. Instead, it first slides on the surface and then lifts off to form the balloon. The problem of simulating the unwinding process can be split into two smaller subproblems: the first task is to describe the motion of the yarn in the balloon; the second one is to solve the sliding motion. In spite of the seemingly complex form of the equations, they can be partially analytically solved as we show in the paper.