In modern engineering, the radial - or belted - tyre has completely replaced the cross -ply tyre. The cords in a radial tyre casing run perpendicular to the direction of travel. Viewed from the side, the cords run radially - giving the tyre its name.
The weakness of this arrangement is that is that the cords cannot sufficiently absorb lateral forces when cornering or circumferential forces when accelerating. To compensate this, the cords must be supported or complemented by other structural elements - steel belts etc.
Diagram above shows a typical radial carcass construction. You can see that the cords of the carcass run at 90 degrees to the perpendicular.