MicroRNAs (miRNAs) are small RNA molecules that modulate gene expression through degradation of specific mRNAs and/or repression of their translation. miRNAs are involved in both physiological and pathological processes, such as apoptosis and cancer. Their presence has been demonstrated in several organisms as well as in viruses. Virus encoded miRNAs can act as viral gene expression regulators, but they may also interfere with the expression of host genes. Viral miRNAs may control host cell proliferation by targeting cell-cycle and apoptosis regulators. Therefore, they could be involved in cancer pathogenesis. Computational prediction of miRNA/target pairs is a fundamental step in these studies. Here, we describe the use of miRiam, a novel program based on both thermodynamics features and empirical constraints, to predict viral miRNAs/human targets interactions. miRiam exploits target mRNA secondary structure accessibility and interaction rules, inferred from validated miRNA/mRNA pairs. A set of genes involved in apoptosis and cell-cycle regulation was identified as target for our studies. This choice was supported by the knowledge that DNA tumor viruses interfere with the above processes in humans. miRNAs were selected from two cancer-related viruses, Epstein-Barr Virus (EBV) and Kaposi-Sarcoma-Associated Herpes Virus (KSHV). Results show that several transcripts possess potential binding sites for these miRNAs. This work has produced a set of plausible hypotheses of involvement of v-miRNAs and human apoptosis genes in cancer development. Our results suggest that during viral infection, besides the protein-based host regulation mechanism, a post-transcriptional level interference may exist. miRiam is freely available for downloading at http://ferrolab.dmi.unict.it/miriam.