  Dissolution fingers (or wormholes) are formed during the dissolution of a
porous rock as a result of nonlinear feedbacks between the flow, transport and
chemical reactions at pore surfaces. We analyze the shapes and growth
velocities of such fingers within the thin-front approximation, in which the
reaction is assumed to take place instantaneously with the reactants fully
consumed at the dissolution front. We concentrate on the case when the main
flow is driven by the constant pressure gradient far from the finger, and the
permeability contrast between the inside and the outside of the finger is
finite. Using Ivantsov ansatz and conformal transformations we find the family
of steadily translating fingers characterized by a parabolic shape. We derive
the reactant concentration field and the pressure field inside and outside of
the fingers and show that the flow within them is uniform. The advancement
velocity of the finger is shown to be inversely proportional to its radius of
curvature in the small P\'{e}clet number limit and constant for large
P\'{e}clet numbers.
