Starting with the classic braid group $B_n$, Birman and Baez have
introduced the monoid $SB_n$ of singular braids where, in addition to the
usual positive and negative crossings $\sg_i$ and $\sg_i^{-1}$ of the
strands at position $i$ and $i+1$, one allows a singular crossing denoted
$\tau_i$ where the two strands intersect. In the same way one can
introduce the singular braid monoid on $\Sigma$, $SB_n(\Sigma)$, as an
extension of the surface braid group $B_n (\Sigma)$. This monoid has been
introduced by Gonz\'alez-Meneses and Paris in order to define finite type
(Goussarov- Vassiliev) invariants for surface braids. They constructed a
universal finite type invariant for surface braids with integer
coefficients. This result cannot be improved. We will show that there does
not exist a universal finite type invariant for surface braids, which is
also fonctorial, i.e. there does not exist a Kontsevich integral for
surface braids. This result does not depend on the choice of the
coefficient ring and it extends naturally to tangles on handlebodies.  
Finally we will discuss about the definition of finite type invariants for
braid groups and their generalisations.