  Applying the Casimir operator to four-point functions in CFTs allows us to
find the conformal blocks for any external operators. In this work, we initiate
the program to find the superconformal blocks, using the super Casimir
operator, for $4D$ ${\mathcal N}=1$ SCFTs. We begin by finding the most general
four-point function with zero $U(1)_R$-charge, including all the possible
nilpotent structures allowed by the superconformal algebra. We then study
particular cases where some of the operators satisfy shortening conditions.
Finally, we obtain the super Casimir equations for four point-functions which
contain a chiral and an anti-chiral field. We solve the super Casimir equations
by writing the superconformal blocks as a sum of several conformal blocks.
