A conventional inertial measurement unit contains three orthogonal accelerometers and three orthogonal gyroscopes to measure acceleration and angular rate of the vehicle. A different possibility is to use a set of distributed accelerometers to measure both acceleration and angular rate. This concept, known as gyro-free navigation, was proposed over 45 years ago and recently arousing a growing interest because of the emergence of low cost MEMS based accelerometers with rapidly increasing performance. Most research in the gyro-free field had focused on seeking optimal accelerometer locations and it appears that less attention was given for deriving appropriate state-space models and analytical error assessment as in a conventional INS. In this paper, we aim to fill this gap. We derive gyro-free kinematic equations expressed in the navigation frame fitting for any set of accelerometer configurations. Such a set may be arbitrary in terms of the number of accelerometers in the configuration, their relative location and orientation. We further derive gyro-free INS error state dynamic equations in a state space model and augment them with dynamic equations representing the accelerometers residuals. In addition, simplified error models and their corresponding closed form solutions, suitable for any gyro-free configurations are derived and their characteristics are analyzed. A case study of six accelerometers configuration is used to illustrate the gyro-free concept and to analyze its performance throughout all the models derived in the paper.