  We define a tower of injections of $\tilde{C}$-type Coxeter groups $W(\tilde
C_{n})$ for $n\geq 1$. We define a tower of Hecke algebras and we use the
faithfulness at the Coxeter level to show that this last tower is a tower of
injections. Let $W^c(\tilde C_{n})$ be the set of fully commutative elements in
$W(\tilde C_{n})$, we classify the elements of $W^c(\tilde C_{n})$ and give a
normal form for them. We use this normal form to define two injections from
$W^c(\tilde C_{n-1})$ into $W^c(\tilde C_{n})$. We then define the tower of
affine Temperley-Lieb algebras of type $\tilde{C }$ and use the injections
above to prove the faithfulness of this tower.
