A process in which force is generated within smooth muscle tissue, resulting in a change in muscle geometry. This process occurs in the gastro-intestinal system. Force generation involves a chemo-mechanical energy conversion step that is carried out by the actin/myosin complex activity, which generates force through ATP hydrolysis. The gastro-intestinal system generally refers to the digestive structures stretching from the mouth to anus, but does not include the accessory glandular organs (liver, pancreas and biliary tract).