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 (so that it is a diamond shape) and sew it into the underarm area of your tunic - it will stretch now when you pull your arm on funny angles.

The way a gusset of this sort works is due to the fact that the diamond-shape is cut "on the bias" - ie the grain of the fabric is running at an angle to the lines of strain/pressure. This means that the threads of the fabric are not pulled tightly against one another (as they would be if the grain of the fabric were running in the same direction as the strain lines), but instead are free to move - which gives the slight amount of stretch that allows freedom of arm-movement.