What are the Core Muscles? Rectus abdominis: Front abdominal muscles. Internal & external obliques: Side of your trunk muscles Erector spinae, multifidus and Quadratus Lumborum: Muscle located between your spine bone and run along your spine & 5. Gluteus muscle: Buttock muscle Your core also includes transverse abdominis, hip muscle, diaphragm, and pelvic floor muscles….