In the lying psoas stretch you hug one knee while lying supine. The other leg is straight, on the floor, and the same side hand reaches away from the foot. This stretches the psoas of the straight leg.
You could do a version of this psoas stretch while standing.
Standing Psoas Stretch | Standing Psoas Stretch Variations
To that end, hug one knee to the chest. activate your pelvic floor muscles and if it isn't already, then flatten your lumbar. Reach your ribs up and the supporting leg arm up. And if it isn't already, straighten the standing knee.
Note that leg rotation, because of where the psoas attaches to the femur, doesn't affect the psoas that much. As such you can try this stretch with your standing foot pointing straight ahead or with it turned out.
In either case what may be more important is pushing the inner thigh back, as described in standing psoas stretch.
While leg rotation may not affect your psoas stretch, moving the legs inwards or outwards can.
So in addition doing this psoas stretch with feet hip width apart, you can also try it with feet together, and also with feet wider apart. The sequence of actions is pretty much the same.
Another variation of this standing psoas stretch is to step one leg back slightly. With the back heel lifted and the back knee straight and pointing down, press the back foot strongly into the floor, as if trying to dig your forefoot in.
You can adjust your hip position from square and level, but when pushing the foot down, keep your pelvis stationary in whatever position you find comfortable for your hips.
Press the foot down after first
Here, the further you move the leg back, the deeper the stretch. This is assuming you keep your spine upright and can keep the lumbar spine flat.
Since rotation doesn't affect the psoas that much (in terms of stretching) you could also do this pose with the back foot turned out and foot flat on the floor.
You could also play with widening the feet side to side (or making your stance more narrow.)
In all cases, when playing around, notice the changes in tension (or feeling) from variation to variation. The more you do this, you may find that you begin to intuitively select and use the best position for you.
Also note, if your psoas gets tight all the time, and not just from exercise, you've probably got a problem. If that's the case, you need to look at finding the problem and fixing that. And that's one reason, for learning to feel and control your body as well as understand it. It gives you the tools to isolate a problem (find it) and fix it.
The Standing Psoas Stretch
More Hip Flexor Stretches
Counter Psoas Stretches with Glute Stretches
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