Dynamics modeling and analysis of a tiny swimming robot, which is composed of a helix type head and an elastic tail, is presented in this paper. The microrobot is designed for controlled drug delivery. It is at the micrometer scale and suitable for a swimming environment under low Reynolds number (Re). The head of the swimming robot is driven by an external rotating magnetic field, which enables it to be operated wirelessly. The spiral-type head accommodates communication and control units and serves as the base for the elastic tail. When a rotating magnetic field is applied, the head rotates synchronously with the field, generating and propagating driving torque to the straight elastic tail. When the driving torque reaches a threshold, dramatic deformation takes place on the elastic tail. The tail then transforms into a helix and generates propulsive thrust. The entire tail also serves as a drug reservoir. This paper focuses on analyzing the dynamics of the microrobot using resistive force theory (RFT), and comparing the propulsion performance with other rigid-body microrobots.