Hey Emma, what happens if you divide by zero, looks like you are doing just that (S and F will become zero at some point in your code). This is not a solution. It's just to allow you see clearly what's going on in the background of your code.
%Generate Matricies (Increase the figure window to see clearly)
f = linspace(-30,20, 30); % some combinations of f and s will include zero
s = linspace(-20,20,30); % in S or F giving an undesirable result, since division
% by zero is not allowed.
[S,F] = meshgrid(s,f);
ss = find(S==0); % Check for zeros in S and F
ff = find(F==0); % Try to make some conditions to avoid dividing by zero.
Z = ((s_u)*(f_u)*E0)./(S.*F.* (s_u-(S.^2)).* (f_u-(F.^2)) );
%Plot
Zmin = min(min(Z));
Zmax = max(max(Z));
spacing = 0.005; % draw more circles between each interval for smaller values
topspace = 1; % increase the upper limit circles
levels=[Zmin:spacing:1,1,1:topspace:Zmax];
contour(F,S,Z,levels);
grid
