A series of new pyrazolo[4,3-e][1,2,4]triazine acyclonucleosides 2–5 and 8 were prepared and evaluated for their anticancer activity against human cancer cell lines (MCF-7, K-562) and CDK2/E, as well as Abl protein kinases inhibitors. Lipophilicity of the compounds was determined using C-18 and immobilized artificial membrane (IAM) chromatography. In order to confirm the molecular structures and synthesis pathway of new acyclonucleosides, X-ray analysis was performed for model compound 3. Theoretical calculations at the DFT/B3LYP/6-311++G(d,p) level were used for the characterization of electronic structures of 1–8. The potential antiviral activity of acyclonucleosides 2–8 was tested in silico using molecular docking method.