Summary form only given, as follows. Liner magnetic implosion experiments usually make use of liners having the shape of right circular cylinder. This paper considers the possibility of using axially symmetric liners of a more complex (concave) shape. As computations show, during concave liner implosion at an appropriate choice of initial curvature (in plane r-z) liner's linear mass can be many times reduced. Such liners can be considered as variable-mass (decreasing mass) liners. The usefulness of the above feature is that it allows a considerable increase in the liner's rate of convergence to the axis as compared to the cylindrical liner of identical initial thickness and identical initial radius. A higher liner velocity at a fixed speed of operation of the current source is desired in a number of practical applications of high-speed liner magnetic implosion (generation of megabar pressures, X-ray pulse, etc.).