According to Timothy Noakes, author of "Lore of Running," a level, relatively soft surface, such as a gravel road, is the best surface for running. The surfaces of parks, streets and sidewalks, such as concrete, asphalt and grass, put a certain amount of strain on your legs but also offer some advantages.
Cement or Concrete
Concrete is among the least forgiving of running surfaces, causing significant shock to your lower-body joints. "Lore of Running" notes that the risk of injury, particularly to women who run, increases on a concrete surface. On the other hand, concrete is often a relatively smooth and regular surface. Generally, the drawbacks of running on a cement-paved surface outweigh the pros over time, and you should avoid training on concrete whenever possible.
Asphalt
Asphalt is one of the fastest surfaces on which you can run. Although it puts some strain on your body, asphalt is significantly more forgiving than concrete as shown in 1992 study published in "Human Movement and Science." Significantly, however, asphalt is difficult to avoid. City streets, park trails, running paths and country roads are all paved with asphalt. The shock forces associated with asphalt are among the lowest available to an urban runner.
Grass
A study in "Human Movement Science" found running on grass to cause a 25 percent greater shock to the musculoskeletal system than running on asphalt. The latter position was cited favorably in the text "Running," and supported by later scientific studies. While running on grass cause little discomfort, as noted, it is not as ideal for your body as running on asphalt.
Considerations
Among cement, asphalt and grass, although it does not offer all the benefits of gravel, asphalt is the best choice of surfaces for a runner. Asphalt offers a smooth, predictable run with minimal impact on you locomotor system. If gravel or a running track are not available options to you, choose asphalt for longer runs. An occasional run over a well-groomed, level grass field is generally not harmful. Avoid concrete if you can, unless training for a race on such a surface. Then train only sparingly on cement to get a feel for it.