Many runners believe that stretching after a run allows to reduce post exercise soreness, as well as risk of future injury. There is actually very little research to support these ideas.
From a physiological point of view, a demanding run will cause micro-tears in major muscle groups. This is perfectly normal. But forcing these muscles to lengthen by stretching might lead to more soreness.
It is more likely that improper warm up, or intensive training can cause that soreness. The whole idea of static stretching is controversial today, as the perceived increase in range of motion may be due to temporary release by the nervous system.
The author suggests to try using the H.E.L.P acronym after the run session
H for Hydrate
E for Easy walk
L for Lie down
P for Pump - small circle movements of solicited joints
As a keen runner, I am gonna try to adopt this for my next running sessions, and try to feel if it makes a difference with the usual stretches I have been doing so far.