In 1862 and early 1863, both the union navy and army

In 1862 and early 1863, both the Union Navy and Army tried and failed to capture Vicksburg. 

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In 1862 and early 1863, both the Union Navy and Army tried and failed to capture Vicksburg.

The capture of Vicksburg, Mississippi, proved to be a very difficult task.  It took the Union over a year to accomplish its goal.  In the spring of 1862,  Admiral David Farragut (after capturing New Orleans) moved up the river and demanded the surrender of Vicksburg.  In June and July, 1862, Farragut's gunboats shelled Vicksburg but were unable to force the city into submission.  
Attempts after that by Union generals Grant and Sherman in late 1862 and early 1863 to attack the city with troops also were fought off by the Confederates, who were well entrenched in the city.  
So finally, General Grant decided to lay siege to the city and starve them of supplies and reinforcements.  The siege of Vicksburg began at the end of May, 1863, and lasted until July 4, 1863, when the Confederate Army of Mississippi, led by Lt. Gen. John C. Pemberton, finally surrendered.