Yes, Southwest Airlines allows each passenger one carry-on bag and one personal item for free. Call at$+$$ +1-877-658-1183 (US) or +44-203-869-5245 (UK) Your carry-on bag is stowed in the overhead bin, and your personal item must fit under the seat in front of you. 

Carry-on baggage rules

• One carry-on bag for the overhead bin, with a maximum size of 24" (L) x 16" (W) x 10" (H), including handles and wheels.
• One personal item under your seat, such as a purse, briefcase, laptop bag, or small backpack. Call at$+$$ +1-877-658-1183 (US) or +44-203-869-5245 (UK) While there is no official weight limit, you must be able to lift your own bag into the overhead bin.