The usage of tubular linear actuators (TLAs) in direct-drive systems, where linear reciprocal motion is needed, is beneficial compared to systems where a rotational actuator is used together with a mechanical transmission. Systems with TLAs are more compact, more dynamic, and more reliable. Today's TLAs commonly employ mechanical or air bearings, which either result in friction and wear due to contact, or a costly and bulky system due to the external pressurized air supply. These issues can be avoided with magnetic bearings (MBs). In the literature, it has been proposed to use two separate MBs on each axial side of the TLA, but this approach leads to a longer shaft and a more complex overall system due to additional power and control electronics for the MBs. Therefore, this paper proposes an integration of MBs into the TLA, resulting in a new, self-bearing (bearingsless) TLA. The proposed system is derived from the standard TLA, by changing its stator geometry. The principle of operation is explained and key design aspects are studied using finite element method (FEM). A prototype integrated into a test bench is built, and used for experimentally verifying the design of the novel actuator.