This paper describes a preliminary investigation into automatic assessment of reading comprehension in young children. In particular we studied the feasibility of automatic scoring of answers to open-ended questions related to the contents of a passage read by a child. Data from 70 children in grades 1 and 2 were used in this work. An automatic speech recognition system, especially trained for children`s speech, was used for tracking the read passage, and two methods for automatic assessment were tested and compared with scores assigned by elementary school teachers. Automatic assessment showed a high kappa statistics agreement with evaluation scores obtained from teachers` scores, K=0.62, comparable to the inter-teacher agreement, K=0.64.