Polyurethanes having improved tear resistance which are the reaction product of the following components: A) a polyol component containing dimer diol and/or trimer triol and/or an OH-terminated polyester produced from polycarboxylic acids, preferably dimer fatty acid and/or trimer fatty acid, and diols and B) an isocyanate component containing prepolymers obtained by reacting polyfunctional isocyanates with dimer diol and/or trimer triol and/or an OH-terminated polyester produced from polycarboxylic acids, preferably dimer fatty acid and/or trimer fatty acid, and diols; and processes for their manufacture.