Changes in the position and alignment of cylindrical objects (shafts, pipes, etc.) in heavy machines from a particular coordinate system or from its aligning counterpart need to be measured accurately to prolong the life of machinery and to avoid large-scale accidents. A method for online measurement of the position of cylindrical objects in a two-dimensional (2-D) plane using linear optical fiber array-based laser triangulation sensors is proposed. A mathematical model was first developed to deduce the 2-D change in position of the target axis using two perpendicularly placed sensors and considering the effect of the curvature of the target surface on measurements. Then, using the formula derived and our recorded experimental data, we have demonstrated the measurement of the 2-D position of a cylindrical object with two developed sensors placed remotely at a 100-mm standoff distance.