„Or, a gate building (Torbau) gules with drawbridge, portculli sable and three towers, upon them little flags Or-gules, the expanded middle tower with a cap and the lateral towers with pitched roofs, between the gate and the border of the shield on each side walls with merlons.“ 
The present arms were granted on February 21, 1939 and are based on a relief on the city hall dating from 1561. The oldest seal of the city dates from the 14th century and shows a tower. Later seals showed the tower behind city walls. All seals and arms of the city showed the castle, first with the single tower, later with the three towers as in the arms. The style of the castle varied according to the style of the times. The colours were not determined until 1939. The present colours are taken from the arms of the Lords of Steinfurt, who became extinct in 1421.
This image is taken from www.ngw.nl – Heraldry of the World –  an international civic heraldry site by Ralf Hartemink. http://www.ngw.nl/int/dld/b/burgstei.htm

Entstehungsgeschichte des Wappens der Stadt Steinfurt
unknown