In this work, we target at the problem of offline sketch parsing, in which the temporal orders of strokes are unavailable. It is more challenging than most of existing work, which usually leverages the temporal information to reduce the search space. Different from traditional approaches in which thousands of candidate groups are selected for recognition, we propose the idea of shapeness estimation to greatly reduce this number in a very fast way. Based on the observation that most of hand-drawn shapes with well-defined closed boundaries can be clearly differentiated from non-shapes if normalized into a very small size, we propose an efficient shapeness estimation method. A compact feature representation as well as its efficient extraction method is also proposed to speed up this process. Based on the proposed shapeness estimation, we present a three-stage cascade framework for offline sketch parsing. The shapeness estimation technique in this framework greatly reduces the number of false positives, resulting in a 96.2% detection rate with only 32 candidate group proposals, which is two orders of magnitude less than existing methods. Extensive experiments show the superiority of the proposed framework over state-of-the-art works on sketch parsing in both effectiveness and efficiency, even though they leveraged the temporal information of strokes.