This paper presents a real-time piano synthesizer where both the transverse and longitudinal motion of the string is modeled by modal synthesis, resulting in a coherent and highly parallel model structure. The paper applies recent developments in piano modeling and focuses on the issues related to practical implementation (e.g., numerical stability, aliasing, and efficiency). A strong emphasis is given to modeling nonlinear string vibrations, and a new variation of earlier synthesis techniques is proposed which is particularly well suited for modal synthesis. For soundboard modeling, the possibilities of using fast Fourier transform-based fast convolution and parallel second-order filters are discussed. Additionally, the paper describes the details of the software implementation and discusses the computational complexity of each model block. The piano model runs on current computer hardware with full polyphony in real time.