Axisymmetric, steady flow of a Newtonian fluid past a solid sphere that is either suspended in a tube by an upflowing liquid (the fluidized sphere problem) or falling in a tube (the falling sphere problem) is determined by finite element analysis. The new results show that several correlations for drag presented in the literature are inaccurate (i) for any value of the ratio of the diameter of the tube to that of the sphere, 1/lambda, when inertial effects are moderate (Re greater than or equal to 30) and (ii) for 1/lambda < 3.3 when Re is small. Two new correlations accounting for wall effects on drag for fluidized and falling spheres are presented that are valid when 0 less than or equal to Re less than or equal to 100 and 12.5 greater than or equal to 1/lambda greater than or equal to 1.42. The effects of lambda and Re on the onset of wake formation and wake characteristics are studied in detail. The results show that, as 1/lambda decreases, the Re for the onset of wake formation increases, whereas the length of the wake decreases. Calculations carried out to simulate the effect of a wire used to support a fluidized sphere show that experimental drag results are correct to within 3%.