1 Samuel 16:14-15 says: The Lord's spirit left Saul, and an evil spirit sent by the Lord tormented him.
On www.learnthebible.org, it says: "Some of the most difficult passages in scripture are those that show God using the devil or evil spirits for His purpose. We know that God is not the cause of wickedness, so it goes against our understanding to think of Him sending evil spirits hither and yon to do His bidding. Yet, we examine scripture and there they are. Let us see if we can make sense of this biblical teaching."
Or is it a matter of figurative language—i.e., figures of speech, Semitisms, colloquialisms, and idioms? Perhaps God did not send the evil spirit, but rather he allowed it to happen, which makes a difference.
I am glad that you brought this up because this passage, according to my personal study, could be a reference to clinical depression. When King Saul's disobedience to God led to the prophet Samuel declaring that his reign as king will come to an end, he snapped mentally. When Goliath came to town, he was so afraid that his anxiety (another cause and symptom of depression) kept him from dealing with the giant. When David slew him, and got so much glory from his destroying the Philistine armies, Saul began to become so jealous that whatever was left of his self-control was slowly eaten away by it. This is another sign of depression: hardly any will-power (which is why I am having trouble trying to overcome some of my bad habits).
All this is all that a demon spirit needs in order to take posession and control of a man's mind. So an evil spirit, allowed by God (just like in Job's story), came and took over Saul whenever he let his mind become filled with self-hatred and guilt over his past sinful actions, and became jealous of David's slow rise to popularity and power in Israel.
This is what the apostle Paul talks about to the Corinthian church when he mentioned in 1 Corinthians about the member of the church that had married his step-mom and said for him to be "delivered unto Satan for the destruction of his flesh." He is talking about an "intervention" (like on A&E) by throwing him out to bring him to the end of his sexual addiction to his step-mom and repentance for his sins. This happened and Paul told the church in 2 Corinthians to welcome him back into the fellowship.