Cylinders play a vital role in representing geometry of environmental and man-made structures. Most existing cylinder fitting methods perform well for outlier free data sampling a full cylinder, but are not reliable in the presence of outliers or incomplete data. Point Cloud Data (PCD) are typically outlier contaminated and incomplete. This paper presents two robust cylinder fitting algorithms for PCD that use robust Principal Component Analysis (PCA) and robust regression. Experiments with simulated and real data show that the new methods are efficient (i) in the presence of outliers, (ii) for partially and fully sampled cylinders, (iii) for small and large numbers of points, (iv) for various sizes: radii and lengths, and (v) for cylinders with unequal radii at their ends. A simulation study consisting of 1000 cylinders of 1 m radius with 20% clustered outliers, reveals that a PCA based method fits cylinders with an average radius of 2.84 m and with a principal axis biased by outliers of 9.65° on average, whereas the proposed robust method correctly estimates the average radius of 1 m with only 0.27° bias angle in the principal axis.