ArrayUtilities.cs

public static class ArrayUtilities
{
    public static void Shift<T>(T[,] array, int x, int y)
    {
        ShiftHorizontal(array, x);
        ShiftVertical(array, y);
    }

    public static void ShiftHorizontal<T>(T[,] array, int x)
    {
        while (x != 0)
        {
            var a = Math.Sign(x);
            switch (a)
            {
                case -1:
                    ShiftLeft(array);
                    break;
                case 1:
                    ShiftRight(array);
                    break;
            }
            x -= a;
        }
    }

    public static void ShiftVertical<T>(T[,] array, int y)
    {
        while (y != 0)
        {
            var a = Math.Sign(y);
            switch (a)
            {
                case -1:
                    ShiftUp(array);
                    break;
                case 1:
                    ShiftDown(array);
                    break;
            }
            y -= a;
        }
    }

    public static void ShiftLeft<T>(T[,] array)
    {
        for (var y = 0; y < array.GetLength(1); y++)
        {
            var end = array[0, y];
            for (var x = 0; x < array.GetLength(0) - 1; x++)
            {
                array[x, y] = array[x + 1, y];
            }
            array[array.GetLength(0) - 1, y] = end;
        }
    }

    public static void ShiftRight<T>(T[,] array)
    {
        for (var y = 0; y < array.GetLength(1); y++)
        {
            var end = array[array.GetLength(0) - 1, y];
            for (var x = array.GetLength(0) - 1; x >= 1; x--)
            {
                array[x, y] = array[x - 1, y];
            }
            array[0, y] = end;
        }
    }

    public static void ShiftUp<T>(T[,] array)
    {
        for (var x = 0; x < array.GetLength(0); x++)
        {
            var end = array[x, 0];
            for (var y = 0; y < array.GetLength(1) - 1; y++)
            {
                array[x, y] = array[x, y + 1];
            }
            array[x, array.GetLength(1) - 1] = end;
        }
    }

    public static void ShiftDown<T>(T[,] array)
    {
        for (var x = 0; x < array.GetLength(0); x++)
        {
            var end = array[x, array.GetLength(1) - 1];
            for (var y = array.GetLength(1) - 1; y >= 1; y--)
            {
                array[x, y] = array[x, y - 1];
            }
            array[x, 0] = end;
        }
    }
}

Seems to work fine :)