The present work shows how data obtained in a depth-sensing indentation test using a Knoop indenter may be analyzed to provide elastic modulus and hardness of the specimen material. The method takes into account the elastic recovery along the direction of the short axis of the residual impression as the indenter is removed. If elastic recovery is not accounted for, the elastic modulus and hardness are overestimated by an amount that depends on the ratio of E/H of the specimen material. The new method of analysis expresses the elastic recovery of the short diagonal of the residual impression into an equivalent face angle for one side of the Knoop indenter. Conventional methods of analysis using this corrected angle provide results for modulus and hardness that are consistent with those obtained with other types of indenters.