Praise be to Allah.
The `awrah (private parts to be necessarily covered) for men includes what is between the navel and the knees as stated by the Prophet SAWS (peace be upon him), so covering it is obligatory according to Islamic law. Wearing shorts that disclose the thighs or show the shape of the buttocks, does not cover the `awrah. Neither does a dress that is transparent and displays skin complexion, nor a tight dress that shows the size, shape or bends of the `awrah. All of this is prohibited (haraam) in front of people whether the women are ashamed of looking at it or not (as asked in the question). If the trousers (or pants) are wide enough and not tight, then one may tuck his shirt in it as long as it does not display his `awrah. Covering the `awrah is obligatory during the prayer and outside it. What many people do is cover their `awrah while going to prayer but are negligent of it outside the prayer. This is a clear mistake and a wrong act which happens due to lack of understanding or as a result of a misunderstanding of the matter.
May Allah cover our sins in this world and in the hereafter.