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The axillary sheath is a fibrous sheath that encloses the first portion of the axillary artery, together with the brachial plexus .The axillary vein lies entirely outside the sheath). It is an extension of the prevertebral fascia of the deep cervical fascia.
A brachial plexus nerve block can be achieved by injecting anaesthetic into this area.
References
Axillary sheath Wikipedia(Text) CC BY-SA