Gussets

A gusset is a small piece of fabric inserted at a place of strain to allow free movement and flexibility without the (non-stretchy) fabric ripping. Most commonly found under the arms, but can also be found in other places (eg modern underwear and lycra pants, period socks at the heel, etc)

The medieval gusset is normally a square of fabric about 8-12cm wide (on average, this can differ - use whatever suits). Turn it diagonally and sew it into the underarm area of your tunic - it will stretch now when you pull your arm on funny angles.