The ongoing paradigm change in the scholarly publication system (‘science is turning to e-science’) makes it necessary to construct alternative evaluation criteria/metrics which appropriately take into account the unique characteristics of electronic publications and other research output in digital formats. Today, major parts of scholarly Open Access (OA) publications and the self-archiving area are not well covered in the traditional citation and indexing databases. The growing share and importance of freely accessible research output demands new approaches/metrics for measuring and for evaluating of these new types of scientific publications. In this paper we propose a simple quantitative method which establishes indicators by measuring the access/download pattern of OA documents and other web entities of a single web server. The experimental indicators (search engine, backlink and direct access indicator) are constructed based on standard local web usage data. This new type of web-based indicator is developed to model the specific demand for better study/evaluation of the accessibility, visibility and interlinking of open accessible documents. We conclude that e-science will need new stable e-indicators.