The endoplasmic reticulum (ER) is a highly dynamic polygonal membrane network composed of interconnected tubules and sheets (cisternae) that forms the first compartment in the secretory pathway involved in protein translocation, folding, glycosylation, quality control, lipid synthesis, calcium signalling, and metabolon formation. Despite its central role in this plethora of biosynthetic, metabolic and physiological processes, there is little quantitative information on ER structure, morphology or dynamics. Here we describe a software package (AnalyzER) to automatically extract ER tubules and cisternae from multi-dimensional fluorescence images of plant ER. The structure, topology, protein-localisation patterns, and dynamics are automatically quantified using spatial, intensity and graph-theoretic metrics. We validate the method against manually-traced ground-truth networks, and calibrate the sub-resolution width estimates against ER profiles identified in serial block-face SEM images. We apply the approach to quantify the effects on ER morphology of drug treatments, abiotic stress and over-expression of ER tubule-shaping and cisternal-modifying proteins.