For an atomic domain $R$, its elasticity $\rho \left(R\right)$ is defined by : $\rho \left(R\right)=sup\{m/n\left|u_1\cdots u_m=v_1\cdots v_n\right.$ for irreducible $u_j,v_i\in R\}$. We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants ${\mu }_m\left(R\right)$ defined by : ${\mu }_m\left(R\right)=sup\{n\left|u_1\cdots u_m=u_1\cdots v_n\right.$ for irreducible $u_j,v_i\in R\}$. As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants ${\mu }_m$ and $\rho$ for monoids and integral domains which are of independent interest.