Here is a wonderful article about casting and carrying burdens written by Anabel Gillham.
Cast or Carry Burdens
Cast or Carry?
When a person comes into your life bringing his bag of problems with him, when a person carries grief and stress and pain into your world, when a person causes chaos over which you have no control, what do you do?
How do you deal with the pressure of painful encounters and fragmented relationships? With angry, rebellious people? With divorce, sickness, bitterness, and death? With loneliness? With the circumstance that you never dreamed would be a part of your life? With the weight of the burden that has worn out your emotions and left you physically exhausted? How do you handle it?
The Bible, our love letter, tells us in Psalm 55:22, “Cast your burden upon the Lord, and He will sustain you.” Let’s paraphrase that: “Get rid of that burden; throw it on the Lord; fling it at His feet. Don’t sneak up to give it to Him. To cast means to throw forcefully. Once you have done that, He promises that He will take care of you, sustain you; He promises to be your sustenance.”
What sort of sustenance is the psalmist talking about here? It’s not physical—not food or drink. I need emotional sustenance. Emotional relief. I need stability, strength, and wisdom. I need peace, the therapy of rest. I need the calmness that comes when I know that everything is under the control of an authority figure, a professional, someone I can trust, someone who knows what to do. That’s exactly the sort of sustenance Psalm 55:22 is talking about.