Determining the grade of colon cancer from tissue slides is a routine part of the pathological analysis. In the case of colorectal adenocarcinoma (CRA), grading is partly determined by morphology and degree of formation of glandular structures. Achieving consistency between pathologists is difficult due to the subjective nature of grading assessment. An objective grading using computer algorithms will be more consistent, and will be able to analyse images in more detail. In this paper, we measure the shape of glands with a novel metric that we call the Best Alignment Metric (BAM). We show a strong correlation between a novel measure of glandular shape and grade of the tumour. We used shape specific parameters to perform a two-class classification of images into normal or cancerous tissue and a three-class classification into normal, low grade cancer, and high grade cancer. The task of detecting gland boundaries, which is a prerequisite of shape-based analysis, was carried out using a deep convolutional neural network designed for segmentation of glandular structures. A support vector machine (SVM) classifier was trained using shape features derived from BAM. Through cross-validation, we achieved an accuracy of 97% for the two-class and 91% for three-class classification.