When a ship runs at the low speed in harbours, steering and propeller operations are often ordered. The hydrodynamic forces generated by the rudder are influenced by various propeller loads and ship speeds, such as ahead and astern propeller loads at forward and backward ship speed. Theoretical investigations and flow observations around the rudder at various propeller loads and ship speeds are carried out to develop the precise mathematical model of the hydrodynamic forces of the rudder. Computer simulations about the elementary manoeuvres in harbours are carried out with the above mathematical models. The results show a good agreement with the experimental results.