Scene text recognition is a challenging problem due to the wide variances in content, style, orientation, and image quality of text instances in natural scene images. To learn the intrinsic representation of scene texts, a novel multi-element attention (MEA) mechanism is proposed to exploit geometric structures from local to global levels in the feature map extracted from a scene text image. The MEA mechanism is a generalized form of self-attention technique with the incorporation of graph structure modeling. The elements in feature maps are taken as the nodes of an undirected graph, and three kinds of adjacency matrices are introduced to aggregating information at local, neighborhood and global levels before calculating the attention weights. If only the local adjacency matrix is used, the MEA mechanism degenerates to a self-attention form. A multi-element attention network (MEAN) is implemented which includes a CNN for feature extraction, an encoder with MEA mechanism and a decoder for predicting text codes. Orientation positional encoding information is further added to the feature map output by the CNN, and a feature sequence as the encoder's input is obtained by element-level decomposition of the feature map. Experimental results show that MEAN has achieved state-of-the-art or competitive performance on public English scene text datasets. Further experiments and analyses conducted on both English and Chinese scene text datasets show that MEAN can handle horizontal, vertical, and irregular scene text samples.