Strength training and flexibility training should go hand in hand. It is a common misconception that there must always be a trade-off between flexibility and strength. Obviously, if you neglect flexibility training altogether in order to train for strength then you are certainly sacrificing flexibility (and vice versa). However, performing exercises for both strength and flexibility need not sacrifice either one. As a matter of fact, flexibility training and strength training can actually enhance one another.
One of the best times to stretch is right after a strength workout such as weightlifting. Static stretching of fatigued muscles (see section Static Stretching) performed immediately following the exercise(s) that caused the fatigue, helps not only to increase flexibility, but also enhances the promotion of muscular development (muscle growth), and will actually help decrease the level of post-exercise soreness. Here's why:
After you have used weights (or other means) to overload and fatigue your muscles, your muscles retain a "pump" and are shortened somewhat. This "shortening" is due mostly to the repetition of intense muscle activity that often only takes the muscle through part of its full range of motion. This "pump" makes the muscle appear bigger. The "pumped" muscle is also full of lactic acid and other by-products from exhaustive exercise. If the muscle is not stretched afterward, it will retain this decreased range of motion (it sort of "forgets" how to make itself as long as it could) and the buildup of lactic acid will cause post-exercise soreness. Static stretching of the "pumped" muscle helps it to become "looser", and to "remember" its full range of movement. It also helps to remove lactic acid and other waste-products from the muscle. While it is true that stretching the "pumped" muscle will make it appear visibly smaller, it does not decrease the muscle's size or inhibit muscle growth. It merely reduces the "tightness" (contraction) of the muscles so that they do not "bulge" as much.
Also, strenuous workouts will often cause damage to the muscle's connective tissue. The tissue heals in 1 to 2 days but it is believed that the tissues heal at a shorter length (decreasing muscular development as well as flexibility). To prevent the tissues from healing at a shorter length, physiologists recommend static stretching after strength workouts.
You should be "tempering" (or balancing) your flexibility training with strength training (and vice versa). Do not perform stretching exercises for a given muscle group without also performing strength exercises for that same group of muscles. Judy Alter, in her book Stretch and Strengthen, recommends stretching muscles after performing strength exercises, and performing strength exercises for every muscle you stretch. In other words: "Strengthen what you stretch, and stretch after you strengthen!"
The reason for this is that flexibility training on a regular basis causes connective tissues to stretch which in turn causes them to loosen (become less taut) and elongate. When the connective tissue of a muscle is weak, it is more likely to become damaged due to overstretching, or sudden, powerful muscular contractions. The likelihood of such injury can be prevented by strengthening the muscles bound by the connective tissue. Kurz suggests dynamic strength training consisting of light dynamic exercises with weights (lots of reps, not too much weight), and isometric tension exercises. If you also lift weights, dynamic strength training for a muscle should occur before subjecting that muscle to an intense weightlifting workout. This helps to pre-exhaust the muscle first, making it easier (and faster) to achieve the desired overload in an intense strength workout. Attempting to perform dynamic strength training after an intense weightlifting workout would be largely ineffective.
If you are working on increasing (or maintaining) flexibility then it is very important that your strength exercises force your muscles to take the joints through their full range of motion. According to Kurz, Repeating movements that do not employ a full range of motion in the joints (like cycling, certain weightlifting techniques, and pushups) can cause of shortening of the muscles surrounding the joints. This is because the nervous control of length and tension in the muscles are set at what is repeated most strongly and/or most frequently.