Subjective screening of children with speech disorders is costly, time consuming and infeasible due to the limited availability of Speech and Language Pathologists (SLPs). Therefore, there is an increasing interest in automatic speech analysis of children with speech disorders as it can offer a practical alternative to human assessment. Paralinguistic features are a set of low-level descriptors commonly used in speech emotion recognition. However, they have not yet been examined with childhood speech sound disorders such as, apraxia-of-speech and phonological and articulation disorders. In this paper, we investigated the effectiveness of paralinguistic features in discriminating between typically developing children and those who suffer from different types of speech sound disorders. Two types of standard paralinguistic features were explored, the Geneva Minimalistic Acoustic Parameter Set (GeMAPS) and its extended version, (eGeMAPS) feature sets. We applied feature selection to find the most discriminant set of features and employed binary classification using a support vector machine (SVM) to discriminate between the two groups. The method was tested on a recently-released public speech corpus collected from typically developing children and children with various types of speech sound disorders. The system achieved segment-level and subject-level unweighted average recall (UAR) of around 78% and 87% respectively.