Inverse rendering is a method for estimating object shapes and lighting conditions from a set of images. In the present paper, we propose an uncalibrated photometric stereo method that approximates the shapes of the target objects using quadric surfaces (ellipsoids or hyperboloids), and this shape representation allows us to use multiple cameras in order to reduce the GBR ambiguity. The proposed method uses the Levenberg-Marquardt method to minimize the differences between the input images and generated images calculated based on the estimated parameters and the image formation model. It is important to define each term in the cost function depending on the inside or outside of the contour of the estimated quadric surface and/or the target object. The proposed method has been verified on several sets of real images, namely, Vase, Grapes, and Snacks, and we found that the method required less than 100 iterations. On the other hand, there is room for improvement regarding the accuracy of the estimation by taking into account the shadows of the target objects and using a more advanced reflection model.