Elastic net is a popular linear regression tool and has many important applications, in particular, finding genomic biomarkers for cancers from gene expression profiles for personalized medicine (elastic net is currently the most accurate prediction method for this problem). There is an increasing trend for organizations to store their data (e.g. gene expression profiles) in an untrusted third-party cloud system in order to leverage both its storage capacity and computational power. Due to the privacy concern, data must be stored in its encrypted form. While there are quite a number of privacy-preserving data mining protocols on encrypted data, there does not exist one for elastic net. In this paper, we propose the first privacy-preserving elastic net protocol using two non-colluding servers. Our protocol is able to handle expression profiles encrypted from multiple medical units using different encryption keys. Thus, collaboration between multiple medical units are made possible without jeopardizing the privacy of data records. We formally prove that our protocol is secure and implemented the protocol. The experimental results show that our protocol runs reasonably fast, thus can be applied in practice.