Christoffer Flensburg, Gösta Gustafson, Leif Lönnblad Elastic and quasi-elastic $pp$ and $\gamma^\star p$ scattering in the Dipole Model Abstract We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes sub-leading effects from energy conservation and running coupling as well as colour suppressed saturation effects from pomeron loops via a dipole swing''. The model was applied to describe the total and diffractive cross sections in $pp$ and $\gamma^*p$ collisions, and also the elastic cross section in $pp$ scattering. In this paper we extend the model to describe the corresponding quasi-elastic cross sections in $\gamma^*p$, namely the exclusive production of vector mesons and deeply virtual compton scattering. Also for these reactions we find a good agrement with measured cross sections. In addition we obtain a reasonable description of the $t$-dependence of the elastic $pp$ and quasi-elastic $\gamma^\star p$ cross sections. LU TP 08-14, arXiv:0807.0325 [hep-ph]