I want to add two circiuts to a junction box , apx 400' from a pass through electrical box on my property, I had put in underground 1 1/4 cunduit with a pull box every 100 feet when the house was built. What size cable should be used for this, it will need to handle 2- 20 amp circuits

What's a "pass through" junction box? Are you splicing into an existing circuit? Or is it actually a subpanel? We need a lot more information.

The panel has power directly from the meter, then a main disconnect (200 amp breaker?) , then bars for breakers and a set of terminals to send power downline to another panel using large cable. There are breakers in this panel I can tap off, for outlets, so on. I currently have a gfi plug mounted on the side of the box, I want to add 2 more circuits, but quite a distance away- 400 ft. I will be using dedicated 20 A breakers for these circuits. Will be for tree lights, gate lights , so on

400 feet is a very long run for 120 volts, even with such a small load.

If you run # 2 copper, with a total max of 40 amp load, the voltage drop will be 5%, which is the max recommended amount.

Now if the load is less than 40 amps, which is more likely the case, the Vd will be less. A 30 amp load will result in 3.8%, to illustrate.