Thank you very much. I will try and get more experiences.

I got it. I had misprints in N1 when I used the simplify(M1-N1). After I corrected I did not try.
But for the substitutions, I hope that all the terms which will form -s1^2+mu1*epsilon1*kappa^2+v^2+u^2(be zero),
and - s2^2+mu2*epsilon2*kappa^2+v^2+u^2 (be zero=0) after combinations will disappear from the expression, not just substitute s1 and s2 by the rhs of the equations.
Any advice?

M1 := (w*(-epsilon2*w+s2)*(-mu1*epsilon1*kappa^2+s1^2-v^2-u^2)*exp(-s1*xp)-w*(s1+w*epsilon1)*(s2^2-mu2*epsilon2*kappa^2-v^2-u^2)*exp(w*a-s2*(a-xp))+(-epsilon2*w+s2)*(-w^2*s1+w*v^2*epsilon1+w*u^2*epsilon1+s1*kappa^2)*exp(-w*xp)+(-s2*kappa^2-w*epsilon2*u^2+w^2*s2-w*epsilon2*v^2)*(s1+w*epsilon1)*exp(w*xp))/(2*kappa^2*w*(w*epsilon1*((1+exp(2*w*a))*s2+(-1+exp(2*w*a))*w*epsilon2)+s1*((-1+exp(2*w*a))*s2+(1+exp(2*w*a))*w*epsilon2)));
N1 := (1/2)*(mu2*epsilon1*exp(-s2*(a-xp))*epsilon2*kappa^2*w^2+mu2*s1*exp(-s2*(a-xp))*epsilon2*kappa^2*w-exp(-w*a)*w^2*epsilon2*v^2*exp(-w*xp)*epsilon1+exp(-w*a)*w*v^2*exp(-w*xp)*epsilon1*s2+exp(-w*a)*w*u^2*exp(-w*xp)*epsilon1*s2-exp(-w*a)*w*epsilon2*exp(-w*xp)*s1*kappa^2-exp(-w*a)*w^2*epsilon2*u^2*exp(-w*xp)*epsilon1-exp(-w*a)*w^2*epsilon2*exp(-s1*xp)*s1^2+exp(-w*a)*epsilon2*exp(-w*xp)*s1*w^3-exp(-w*a)*mu1*exp(-s1*xp)*epsilon1*kappa^2*s2*w+exp(-w*a)*mu1*epsilon2*exp(-s1*xp)*epsilon1*kappa^2*w^2-exp(-w*a)*w*u^2*exp(-s1*xp)*s2-exp(-w*a)*w*exp(-s1*xp)*v^2*s2+exp(-w*a)*exp(-w*xp)*s1*kappa^2*s2-exp(-w*a)*w^2*exp(-w*xp)*s1*s2+exp(-w*a)*w*exp(-s1*xp)*s1^2*s2+exp(-w*a)*w^2*epsilon2*u^2*exp(-s1*xp)+exp(-w*a)*w^2*epsilon2*exp(-s1*xp)*v^2-w*epsilon1*exp(-w*(a-xp))*s2*kappa^2-w*epsilon2*s1*exp(-w*(a-xp))*v^2-w*epsilon2*u^2*s1*exp(-w*(a-xp))-w^2*epsilon2*v^2*epsilon1*exp(-w*(a-xp))-w^2*epsilon2*u^2*epsilon1*exp(-w*(a-xp))+w*v^2*s1*exp(-s2*(a-xp))-w*s1*exp(-s2*(a-xp))*s2^2+w^2*s1*s2*exp(-w*(a-xp))-s1*exp(-w*(a-xp))*s2*kappa^2+w^2*v^2*epsilon1*exp(-s2*(a-xp))+w^2*u^2*epsilon1*exp(-s2*(a-xp))-w^2*epsilon1*exp(-s2*(a-xp))*s2^2+w*u^2*s1*exp(-s2*(a-xp))+epsilon1*s2*exp(-w*(a-xp))*w^3)/(kappa^2*(exp(w*a)*w^2*epsilon1*epsilon2+exp(w*a)*w*epsilon1*s2-exp(-w*a)*w^2*epsilon1*epsilon2+w*s2*epsilon1*exp(-w*a)+exp(-w*a)*s1*epsilon2*w-s2*s1*exp(-w*a)+s1*exp(w*a)*epsilon2*w+s1*exp(w*a)*s2)*w);
I hope to show that they are equal by some symbolic simplifications. And then I want to substitute s1^2=mu1*epsilon1*kappa^2+v^2+u^2, s2^2=mu2*epsilon2*kappa^2+v^2+u^2 in either of the two. Please give me a hand. Thanks in advance.

Thanks acer, I will try. I think it must have misprints, for I need them to be the same.

Thanks Jean. I reinstalled Maple and works now.