  A Banach space $X$ is elastic if there is a constant $K$ so that whenever a
Banach space $Y$ embeds into $X$, then there is an embedding of $Y$ into $X$
with constant $K$. We prove that $C[0,1]$ embeds into separable infinite
dimensional elastic Banach spaces, and therefore they are universal for all
separable Banach spaces. This confirms a conjecture of Johnson and Odell. The
proof uses incremental embeddings into $X$ of $C(K)$ spaces for countable
compact $K$ of increasing complexity. To achieve this we develop a
generalization of Bourgain's basis index that applies to unconditional sums of
Banach spaces and prove a strengthening of the weak injectivity property of
these $C(K)$ that is realized on special reproducible bases.
