This thesis is about synthesizing the sound of keyboard instruments based on a physical model. The three instruments that will be used are the grand piano, upright piano and the harpsichord. Their similarities allow for a common, unified model to simulate their sound production. Their differences are captured in the set of parameters, these are responsible for the unique sound of the particular instrument. The main difference between the three instruments is that the harpsichord is a plucked string instrument, the grand and upright piano are struck string instruments. In the beginning of the thesis, I collect the important physical properties of the instruments, with special attention to the excitation mechanism, the string, and the parts that radiate the sound out to the air: the soundboard and the enclosure. The applied physical modeling technique will be the digital waveguide, more precisely the commuted piano synthesis model. The hammer model is the linearized hammer modell proposed in the commuted piano synthesis method. The pluck model used is a simple triangular displacement curve, taking into account multiple plucking points. The elements of the string model are a single delay line, a one pole loss filter, a ripple filter, a dispersion filter and a fractional delay filter. The impulse response of the soundboard is convolved with the excitation signal, and presents the input to the string model. I have implemented one and two stringed models with a coupling scheme. These were implemented using Matlab and partly Simulink. For the real time implementation, I used a Texas Instruments C6713 DSP Started Kit. I used the floating point processor, internal ram and the audio codec, and after the sound synthesis, I implemented a monophonic score player system, that allows the user to choose the instrument played while running, and set the output volume. The model parameters and input sound files are generated by Matlab using real recordings for the offline simulation and real time synthesis as well. The final results are unfortunately not convincingly close to the sound of the original instruments, even after a lot of attempts at fine tuning. The reason for this probably lies in the parameters of the model. Further development efforts should target tuning the elements of the string model separately for each note, refining the pluck model to better simulate the friction in the string after the moment of plucking, and implementing the nonlinear hammer model.