This study presents a method for analyzing speech rhythm using empirical mode decomposition of the speech amplitude envelope, which allows for extraction and quantification of syllabic- and supra-syllabic time-scale components of the envelope. The method of empirical mode decomposition of a vocalic energy amplitude envelope is illustrated in detail, and several types of rhythm metrics derived from this method are presented. Spontaneous speech extracted from the Buckeye Corpus is used to assess the effect of utterance length on metrics, and it is shown how metrics representing variability in the supra-syllabic time-scale components of the envelope can be used to identify stretches of speech with targeted rhythmic characteristics. Furthermore, the envelope-based metrics are used to characterize cross-linguistic differences in speech rhythm in the UC San Diego Speech Lab corpus of English, German, Greek, Italian, Korean, and Spanish speech elicited in read sentences, read passages, and spontaneous speech. The envelope-based metrics exhibit significant effects of language and elicitation method that argue for a nuanced view of cross-linguistic rhythm patterns.