System identification algorithms currently require a full data set, i.e., no missing observations, to estimate the natural vibration properties of a structural system. These algorithms are often based on parameters estimated from a state-space model. There are circumstances in which a Missing Data Problem can arise during data collection; therefore, it is important to adjust these algorithms to facilitate Structural Modal Identification. Despite having missing observations, state-space parameters can be estimated for a time series; subsequently, structural modal properties can be identified. This paper will use the EM algorithm to identify structural modal properties from a data set with missing observations. The end of the paper will focus on the search for a missingness threshold which can be used to assess the probability of extracting useful structural modal properties from a given data set with missing observations. This assessment will be based on the accuracy of modal estimates for data sets with varying magnitudes and patterns of missingness. It is clear that missingness can only reduce the accuracy of modal estimates; however, it is important to establish the associated scale and behavior of the reduction. An example is presented to illustrate the main concepts of this approach.