Why do we suffer abdominal pain after we get very angry or stress?
Cortisol produced from the zona fasciculata of the adrenal cortex is directly caused by stress.

According to http://en.wikipedia.org/wiki/Cortisol


  Cortisol stimulates gastric-acid secretion. Cortisol's only direct effect on the hydrogen ion excretion of the kidneys is to stimulate the excretion of ammonium ions by deactivating the renal glutaminase enzyme. Net chloride secretion in the intestines is inversely decreased by cortisol in vitro.


This increase in gastric-acid secretion can irritate the lining of the GI tract, especially if there are ulcers or inflammation, resulting in pain. In addition, the fight-or-flight response causes 


  inhibition of stomach and upper-intestinal action to the point where digestion slows down or stops.


(see http://en.wikipedia.org/wiki/Fight-or-flight_response)

Those things, paired with increased muscle tension and vasoconstriction cause pressure changes in the GI tract, which can cause pain.