Handstand pushup should be done with hands shoulder width apart . The movement begins with head in contact with the floor and ends with hands in line with the top of the head.

Box handstand pushups

Elevate your feet on a box to end up with feet horizontal with your hips at a 90 degrees. Your arms should be completley straight. Your hips should be above your shoulders. Simple lower down and touch the head to the ground.
The head should remain between arms during the entire movement: keep you ears next your arms

Negative handstand pushups

From a handstand lower your body slowly and with control. The slower you are, the greater the srength is required. Upon reaching the ground stand and kick back to the handstand for the next repetition.

Elevated handstand pushups

In this handstand pushup variation, you will begin to develop true strength over a full range of motions. Using a panel mat or tow blocks.

Korean handstand pushups

On a single bar kick up into normal handstand and then descend with the shoulders lowering completely to the hands. It can be done on wall or with the assistance of a partner.
You can also do the Korean handstand pushups using an under-grip, which makes it more difficult.

Bulgarian handstand pushup on parallel bars

Begin facing both bars from the side. While maintaining your shoulder width, reach your left hand forward and grasp the bar in an over-grip. Grasp the other bar in an under-grip and then go up using the assistance of a partner. When you descend, you should allow your elbows to flare out to the sides. Pause at the bottom and then press back out again.

Gymnastic rings handstand pushups

You can start this exercise by wrapping your feet around the straps and then start from locked arms handstand with rings turned outward. While you are descending, allow your feet to slide down the straps. Pause then press back to handstand.

Another variation of gymnastic rings handstand pushups is to allow you arms to go out as wide as you lower to the bottom of handstand.

When you are confident you don’t need the support of the straps, go for the free handstand. The ring should be turned outward. Descent into the handtsand allowing the rings to turn inward. Pause at the bottom and press back to handstand.

Parallel bars handstand pushups

Begin from a freestanding handstand on the parallel bars or paralletes. As you descend, allow the shoulders to move slightly forward while allowing the legs to drop slightly behind you. Pause at the bottom and press back to handstand.