This paper unifies the approaches of kinematic and static modelling, and singularity analysis for tendon-driven parallel continuum robots under constant curvature as well as pseudo-rigid-body assumptions with those implemented in conventional rigid parallel robots. Constraint conditions are determined for the legs of this type of parallel continuum robots, based on which the velocity equations and Jacobian matrices are derived. These are further exploited for inverse kinematic and singularity analysis. Static models for the robot as well as for each of the continuum links under pseudo-rigid-body assumption are derived. Finally, a simulation example is given to validate the kinematic models. It is shown that singularities can be determined using Grassmann line geometry or by detecting the numerical values of three performance indices.