Soft actuators, designed for fragile item conveyance and navigation in complex environments, have garnered recent attention. This study proposes a cost-effective soft actuator, created by weaving tubes into twill patterns, capable of transportation and movement. The actuator achieves this by inducing traveling waves on its upper and lower surfaces through sequential pressurization of tubes. Notably, its fabrication does not require specialized molds, contributing to cost efficiency. The single actuator generates traveling waves with two degrees of freedom. Conventional silicone tube-based actuators demonstrate slow transport speeds (3.5 mm/s). To address this, this study replaced silicone tubes with pneumatic artificial muscles, enhancing overall body deformation and actuator speed. Experiments involving both extensional and contractional artificial muscles demonstrated that soft actuators with extensional artificial muscles significantly improved transportation and movement speed to 8.0 mm/s.