Smooth-ride pneumatic, semipneumatic, and flat-free plate casters have air-filled, foam-filled, or solid-rubber caster wheels that allow them to absorb more shock and vibration, provide more stability, and produce less noise than other types of plate casters. These casters are suitable for transporting fragile or vibration-sensitive loads and for moving loads over rough or uneven surfaces in outdoor areas and industrial facilities. The casters have a mounting plate that mounts onto the bottom of carts and other equipment to allow the equipment to roll, reducing the effort it takes to move or reposition the equipment. They come in swivel and rigid versions. The swivel casters can rotate 360°, allowing equipment to change directions while rolling. The rigid casters roll in a straight line. Two rigid plate casters can be paired with two swivel casters to allow the equipment to both maneuver around curves and obstacles and maintain a straight course while rolling.