Adho Mukha Vrksasana (Handstand) is not a particularly difficult pose physically. The real challenge of Handstand for many students is working on the necessary physical skills in a calm, focused manner while confronting the primal human fear of falling.
Handstand, like all balancing poses, requires that you feel comfortable with instability. When faced with instability of any kind—physical or mental—most of us tend to recoil immediately and try to regain control by locking things tightly in place. Ironically, this reaction only serves to make us more rigid and less able to make minute and sensitive adjustments to bring ourselves back into balance.
Instead, try to bring a childlike enthusiasm to your Handstand explorations, focusing on the process rather than the outcome. Imagine the solidity of bone paired with the cushiony, more resilient quality of muscle: a secure firmness merged with a more fluid, I-can-respond-instantly-to-anything feeling. As you let yourself yield to gravity without collapsing, you can go inside and find a balanced energy flow that supports the posture.