Write a program that displays the following menu:

1 = Square
2 = Circle
3 = Ellipse
4 = End program

When the user selects a shape from the menu, the program should ask for any necessary data, either:
the length of the square’s side,
the circle’s radius, or
the ellipse's X-radius and Y-radius
and then it should draw that shape in the center of the screen.

Use a loop to repeat this process until the user enters 4.

To write a program that displays the menu and allows the user to select a shape to draw, you can use a loop to repeat the process until the user enters "4". Here's an example of how you can write this program in Python:

```python
import turtle

def draw_square(length):
turtle.penup()
turtle.goto(-length/2, -length/2)
turtle.pendown()
for _ in range(4):
turtle.forward(length)
turtle.right(90)

def draw_circle(radius):
turtle.penup()
turtle.goto(0, -radius)
turtle.pendown()
turtle.circle(radius)

def draw_ellipse(x_radius, y_radius):
turtle.penup()
turtle.goto(-x_radius, -y_radius)
turtle.pendown()
for _ in range(2):
turtle.circle(x_radius, 90)
turtle.circle(y_radius, 90)

def main():
while True:
print("1 = Square")
print("2 = Circle")
print("3 = Ellipse")
print("4 = End program")

choice = input("Enter your choice: ")

if choice == "4":
break

if choice == "1":
length = float(input("Enter the length of the square's side: "))
draw_square(length)
elif choice == "2":
radius = float(input("Enter the circle's radius: "))
draw_circle(radius)
elif choice == "3":
x_radius = float(input("Enter the X-radius of the ellipse: "))
y_radius = float(input("Enter the Y-radius of the ellipse: "))
draw_ellipse(x_radius, y_radius)

turtle.clear()

turtle.done()

if __name__ == "__main__":
main()
```

This program uses the turtle graphics module to draw the shapes. The `draw_square`, `draw_circle`, and `draw_ellipse` functions are defined to draw the respective shapes at the center of the screen. The `main` function prompts the user to select a shape from the menu and then calls the appropriate function based on the user's input. When the user selects "4", the loop exits, and the program ends.

You can run this program and test it by selecting different shapes from the menu and entering the required data. The shape will be drawn at the center of the turtle graphics window.