Vehicle arresting beds, for installation at the ends of aircraft runways, are effective to safely decelerate aircraft entering the bed. The arresting bed is assembled of a large number of blocks of cellular concrete having predetermined compressive gradient strength, so that aircraft landing gear is subjected to drag forces effective to slow a variety of types of aircraft, while providing deceleration within a safe range of values. An arresting bed typically includes an entry region of a depth increasing from 9 to 24 inches formed of blocks having a first compressive gradient strength. A second region, which may be tapered into the first region and increase in depth to 30 inches, is formed of blocks having a greater compressive gradient strength. An aircraft thus experiences increasing drag forces while it travels through the bed, to provide an arresting capability suitable for a variety of aircraft. Arresting bed systems may include composite blocks including portions of cellular concrete of different strengths, reinforced blocks including a lower layer or grid of higher strength material, and cellular concrete block edge members surrounding a bed of aggregate or poured in place cellular concrete.