From the Billy Graham devotional daily calendar:
I've been told that the French translation of this phrase, "Cast all your care upon Him" is "Unload your distresses upon God." Have you ever seen a dump truck get rid of its load? The driver simply pushes a button or pulls on a lever and the heavy load is discharged at the prescribed spot.... We we never meant to be crushed under the weight of care.... Unload the anxieties of the present moment upon Him, for He cares for you. If He loved you enough to take away the burden of your sins, can't you trust Him to take away every lesser burden as well?