This paper describes an approach to the detection of stress in spoken New Zealand English. After identifying the vowel segments of the speech signal, the approach extracts two different sets of features -- prosodic features and vowel quality features -- from the vowel segments. These features are then normalised and scaled to obtain speaker independent feature values that can be used to classify each vowel segment as stressed or unstressed. We used Decision Trees (C4.5) and Support Vector Machines (LIBSVM) to learn stress-detecting classifiers with various combinations of the features. The approach was evaluated on 60 adult female utterances with 703 vowels and a maximum accuracy of 84.72% was achieved. The results showed that a combination of features derived from duration and amplitude achieved the best performance but the vowel quality features also achieved quite reasonable results.