Helium is widely used as a fuel or minority gas in laboratory fusion experiments, and will be present as ash in DT thermonuclear plasmas. It is therefore essential to have a good understanding of its atomic physics. To this end He II population modelling has been undertaken for the spectroscopic levels arising from shells with principal quantum number n = 1-5. This paper focuses on a collisional excitation model; ionisation and recombination will be considered in a subsequent article. Heavy particle collisional excitation rate coefficients have been generated to supplement the currently-available atomic data for He II, and are presented for proton, deuteron, triton and alpha-particle projectiles. The widely-used criterion for levels within an n shell being populated in proportion to their statistical weights is reassessed with the most recent atomic data, and found not to apply to the He II levels at tokamak densities (10(18)-10(21) m(-3)). Consequences of this and other likely sources of errors are quantified, as is the effect of differing electron and ion temperatures. Line intensity ratios, including the so-called 'branching ratios' and the fine-structure beta(1), beta(2), beta(3), and gamma ratios, are discussed, the latter with regard to their possible use as diagnostics.