I like the imagery of taking the things that I'm worried about and throwing them on God. That's what the word "cast" means in the original language. Peter is telling his readers to throw their worries on God and let him take care of them.
I use a mental exercise to try and deal with the stress in my life. When I've got something that I'm worried about, I try to imagine something that represents that concern. If I'm worried about my health, I might think of a hospital or a bottle of pills. If it's a financial problem, I picture a stack of money. It doesn't really matter what I choose, as long as it is something that I can visualize.
Next, I take that symbol of worry, and I imagine that I'm placing it in a burlap sack. I proceed to close the sack, whirl it a few times in my mind, then toss it to God. I visualize myself casting that anxiety on him.
It may sound silly, but I find that the visualization process helps me do what I need to do: stop worrying and trust that God will handle my problems.
The apostle Paul wrote:
Do not be anxious about anything, but in everything, by prayer and petition, with thanksgiving, present your requests to God. And the peace of God, which transcends all understanding, will guard your hearts and your minds in Christ Jesus (Philippians 4:6-7).
If I can learn to turn my worries over to God, he will give me his peace — that divine peace that defies all logic. I decide to give my cares to God, I pray about them, and I thank him for handling them. In return, he gives me peace.
I don't know about you, but I much prefer peace to worry!
So next time something is weighing on your mind, try the mental exercise I described. Combine that with prayer and thanksgiving. You very well may find that God takes your worry away and gives you his peace to replace it.