The surface is called a one-sided surface if the tangent space local orientation changes sign along a closed curve on a surface. The Mobius strip is the simplest one-sided surface. Klein bottle and cross cap are also one-sided surfaces. The Klein bottle can be considered as two Mobius strips glued together at the edge. In this paper, the Klein bottle is cut into two Mobius strips. The Klein bottle in E³ has selfintersection. A closed curve is defined on a thorus in E³ using 4π-periodic vector-function. Equations for Mobius strips and Klein bottle are derived using the defined curve function. If a midline of Mobius strips degenerates into a point, we get crosscap. Also, a twisted Klein bottle and two twisted Mobius strips are constructed with a mathematical software package.