For developing a general theory for design and analysis of soft continuum robot, this paper addresses a general structural pattern (GSP) based on the locomotion features of current continuum soft robots and the longitudinal muscle of slim creatures in the nature, and the corresponding kinematics of continuum soft robots in actuation space, configuration space and task space. To implement dexterous movement and operation by a continuum soft robot in configuration space, a shape reproduction algorithm for a slim soft robot to reproduce arbitrary curves and a shape similarity criterion for evaluating curves reproduction using discrete Fréchet distance are proposed as well. To verify the validity of GSP and its kinematics, simulations and experiments are carried out, using a modular continuum soft robot consisting of two soft modules actuated by SMA (shape memory alloy) springs. Moreover, taking the biomimetic movement curves as the objective curves, the effects of curve shape, section number and parameters on the reproduction performance are studied through many cases. It is shown that the more the soft section modules and the larger the maximum bending angle of a single section, the higher the shape similarity a continuum soft robot achieves.